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6
Verklein
Vergroot
Pagina terug
1/431
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TI-86
GRAPHING CALCULATOR
GUIDEBOOK
TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power
Down, APD, and EOS are trademarks of Texas Instruments Incorporated.
Windows is a registered trademark of Microsoft Corporation.
IBM is a registered trademark of International Business Machines Corporation
Macintosh is a registered trademark of Apple Computer, Inc.
Copyright © 1997, 2001 by Texas Instruments Incorporated
ii
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Important
Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of
merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available
solely on an “as-is” basis.
In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in
connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas
Instruments, regardless of the form of action, shall not exceed the purchase price of this equipment. Moreover, Texas
Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
US FCC Information Concerning Radio Frequency Interference
This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC
rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This
equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the
instructions, may cause harmful interference with radio communications. However, there is no guarantee that interference will
not occur in a particular installation.
If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the
equipment off and on, you can try to correct the interference by one or more of the following measures:
Reorient or relocate the receiving antenna.
Increase the separation between the equipment and receiver.
Connect the equipment into an outlet on a circuit different from that to which the receiver is connected
.
Consult the dealer or an experienced radio/television technician for help.
iii
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Table of Contents
TI
-
86 Quick Start 1
Preparing to Use Your New TI
-
86 .....................................................2
Installing the AAA Batteries .........................................................2
Turning On and Turning Off the TI
-
86..........................................2
Adjusting the Contrast .................................................................2
Resetting All Memory and Defaults..............................................3
Calculating on the Home Screen....................................................... 3
Calculating the Sine of a Number.................................................3
Storing the Last Answer to a Variable.......................................... 3
Using a Variable in an Expression ................................................ 4
Editing an Expression ...................................................................4
Displaying a Complex Number as a Result................................... 5
Using a List with a Function.........................................................5
Displaying the Integer Part of Real Numbers in a List ..................6
Removing (Exiting) a Menu.......................................................... 6
Finding the Square Root...............................................................7
Calculating Derivatives.................................................................7
Retrieving, Editing, and Re-evaluating the Previous Entry ...........8
Converting Degrees Fahrenheit to Degrees Celsius...................... 8
Storing an Unevaluated Expression to an Equation Variable .......9
Plotting Functions on the Graph Screen............................................ 9
Displaying and Entering Functions in the Equation Editor............9
Changing the Graph Style of a Function.....................................10
Plotting a Function on the Graph Screen....................................11
Tracing a Function......................................................................11
Evaluating y for a Specific x Value (During a Trace) ...................12
Changing a Window Variable Value...........................................12
Deselecting a Function ...............................................................13
Zooming In on a Portion of the Graph Screen ............................14
Chapter 1: Operating the TI
-
86 15
Installing or Replacing Batteries .....................................................16
When to Replace Batteries .........................................................16
Turning On and Turning Off the TI
-
86.............................................17
Adjusting the Display Contrast........................................................17
The Home Screen ............................................................................18
Displaying Entries and Answers..................................................18
Entering Numbers ...........................................................................19
Entering Negative Numbers .......................................................19
Using Scientific or Engineering Notation....................................20
Entering Complex Numbers........................................................20
Entering Other Characters...............................................................21
The 2nd Key................................................................................21
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-
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The ALPHA Key........................................................................... 21
ALPHA-lock and alpha-lock........................................................22
Common Cursors........................................................................22
Cursor Direction Keys .................................................................23
Inserting, Deleting, and Clearing Characters.............................. 23
Entering Expressions and Instructions ............................................24
Entering an Expression............................................................... 24
Using Functions in Expressions .................................................. 25
Using an Instruction ...................................................................25
Entering Functions, Instructions, and Operators ........................ 25
Entering Consecutive Entries......................................................26
The Busy Indicator...................................................................... 26
Interrupting a Calculation or Graph ........................................... 26
Diagnosing an Error ........................................................................ 27
Correcting an Error.....................................................................27
Reusing Previous Entries and the Last Answer ............................... 28
Retrieving the Last Entry ............................................................ 28
Retrieving and Editing the Last Entry ......................................... 28
Retrieving Previous Entries......................................................... 28
Retrieving Multiple Entries.........................................................29
Clearing the ENTRY Storage Area .............................................. 29
Retrieving the Last Answer ........................................................29
Using Ans Preceding a Function................................................. 30
Storing Results to a Variable ......................................................30
Using TI
-
86 Menus..........................................................................31
Displaying a Menu......................................................................31
The Menu Keys...........................................................................32
Selecting a Menu Item................................................................32
Exiting (Removing) a Menu ........................................................33
Viewing and Changing Modes ........................................................34
Changing a Mode Setting...........................................................34
Chapter 2:
The CATALOG, Variables, and Characters 37
The CATALOG .................................................................................38
Storing Data to Variables ................................................................39
Creating a Variable Name ..........................................................39
Storing a Value to a Variable Name ...........................................40
Storing an Unevaluated Expression............................................40
Storing an Answer......................................................................41
Copying a Variable Value ...........................................................41
Displaying a Variable Value........................................................41
Recalling a Variable Value..........................................................42
Classifying Variables as Data Types. ...............................................42
The CATLG-VARS (CATALOG-Variables) Menu...........................43
Selecting a Variable Name .........................................................44
The CUSTOM Menu.........................................................................44
Entering CUSTOM Menu Items...................................................44
Clearing CUSTOM Menu Items...................................................45
Deleting a Variable from Memory ..............................................45
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The CHAR (Character) Menu........................................................... 45
The CHAR MISC (Miscellaneous) Menu...................................... 46
The CHAR GREEK Menu.............................................................46
The CHAR INTL (International) Menu.........................................46
Adding a Modifier to a Vowel .................................................... 46
Chapter 3:
Math, Calculus, and Test Operations 47
Keyboard Mathematical Functions .................................................48
The MATH Menu.............................................................................49
The MATH NUM (Number) Menu...............................................49
The MATH PROB (Probability) Menu..........................................50
The MATH ANGLE Menu............................................................51
The MATH HYP (Hyperbolic) Menu.............................................51
The MATH MISC (Miscellaneous) Menu.....................................52
The Interpolate
à
Extrapolate Editor............................................53
The CALC (Calculus) Menu.............................................................. 54
The TEST (Relational) Menu............................................................ 55
Using Tests in Expressions and Instructions ...............................56
Chapter 4: Constants,
Conversions, Bases, and Complex Numbers 57
Using Built-In and User-Created Constants..................................... 58
The CONS (Constants) Menu......................................................58
The CONS BLTIN (Built-In Constants) Menu...............................58
Creating or Redefining a User-Created Constant .......................60
The Constant Editor Menu..........................................................60
Entering a Constant Name in an Expression ..............................61
Converting Units of Measure ..........................................................61
Converting a Unit of Measure ....................................................61
The CONV (Conversions) Menu ..................................................62
The CONV LNGTH (Length) Menu ..............................................63
The CONV AREA Menu...............................................................63
The CONV VOL (Volume) Menu..................................................63
The CONV TIME Menu................................................................63
The CONV TEMP (Temperature) Menu .......................................63
The CONV MASS Menu ..............................................................64
The CONV FORCE Menu.............................................................64
The CONV PRESS (Pressure) Menu .............................................64
The CONV ENRGY (Energy) Menu ..............................................64
The CONV POWER Menu............................................................64
The CONV SPEED Menu .............................................................64
Converting a Value Expressed as a Rate ....................................65
Number Bases .................................................................................65
Number Base Ranges .................................................................66
One’s and Two’s Complements ..................................................66
The (Number) BASE Menu..........................................................66
The BASE
Õ
-
Ú
(Hexadecimal Characters) Menu.........................67
Entering Hexadecimal Digits.......................................................67
The BASE TYPE Menu.................................................................67
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-
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The BASE CONV (Conversion) Menu ..........................................68
Converting Number Bases..........................................................68
The BASE BOOL (Boolean) Menu ............................................... 68
Results of Boolean Operations ...................................................69
The BASE BIT Menu.................................................................... 69
Using Complex Numbers................................................................. 70
Complex Results.........................................................................70
Using a Complex Number in an Expression................................71
The CPLX (Complex Number) Menu...........................................71
Chapter 5: Function Graphing 73
Defining a Graph.............................................................................74
Setting the Graph Mode .................................................................74
The GRAPH Menu ........................................................................... 75
Using the Equation Editor ...............................................................76
The Equation Editor (GRAPH y(x)=) Menu ................................. 76
Defining a Function in the Equation Editor ................................77
Notes about Defining Function Equations.................................. 78
Selecting Graph Styles................................................................ 79
Setting the Graph Style in the Equation Editor........................... 80
Using Shading Patterns to Differentiate Functions.....................80
Viewing and Changing On
à
Off Status of Stat Plots ...................81
Setting the Window Variables......................................................... 81
Displaying the Window Editor....................................................82
Changing a Window Variable Value........................................... 82
Setting Graphing Accuracy with
@
x and
@
y ...............................83
Setting the Graph Format................................................................83
Displaying a Graph..........................................................................85
Pausing or Stopping a Graph in Progress ...................................85
Modifying a Drawn Graph..........................................................85
Graphing a Family of Curves ......................................................86
Smart Graph ...............................................................................86
Chapter 6: Graph Tools 87
Graph Tools on the TI
-
86 ................................................................88
The GRAPH Menu.......................................................................88
Using the Free-Moving Cursor....................................................89
Graphing Accuracy .....................................................................89
Tracing a Graph...............................................................................90
Stopping and Resuming a Trace.................................................91
Resizing the Graph Screen with ZOOM Operations.........................91
The GRAPH ZOOM Menu ...........................................................91
Defining a Custom Zoom In........................................................93
Setting Zoom Factors..................................................................93
Zooming In and Zooming Out on a Graph..................................93
Storing and Recalling Zoom Window Variable Values................95
Using Interactive Math Functions ...................................................95
The GRAPH MATH Menu............................................................95
Settings That Affect GRAPH MATH Operations ..........................96
Using ROOT, FMIN, FMAX, or INFLC ..........................................97
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Using
f(x), DIST, or ARC ............................................................98
Using dy
à
dx or TANLN...............................................................99
Using ISECT ..............................................................................100
Using YICPT.............................................................................. 100
Evaluating a Function for a Specified x......................................... 101
Drawing on a Graph......................................................................101
Before Drawing on a Graph .....................................................102
Saving and Recalling Drawn Pictures .......................................102
Clearing Drawn Pictures........................................................... 103
The GRAPH DRAW Menu ......................................................... 103
Shading Areas of a Graph ........................................................104
Drawing a Line Segment ..........................................................105
Drawing a Vertical or Horizontal Line ......................................106
Drawing a Circle....................................................................... 106
Drawing a Function, Tangent Line, or Inverse Function ........... 107
Drawing Freehand Points, Lines, and Curves ...........................107
Placing Text on a Graph...........................................................108
Turning On or Turning Off Points .............................................108
Chapter 7: Tables 109
Displaying the Table......................................................................110
TABLE Menu............................................................................. 110
The Table.................................................................................. 110
Independent and Dependent Variables in the Table ................111
Navigating the Table................................................................111
The Table Menus ......................................................................112
Setting Up the Table .....................................................................113
Viewing and Editing Dependent Variable Equations ...............114
Clearing the Table.........................................................................114
Chapter 8: Polar Graphing 115
Preview: Polar Graphing ...............................................................116
Defining a Polar Graph..................................................................117
Setting Polar Graphing Mode...................................................117
The GRAPH Menu.....................................................................117
Displaying the Polar Equation Editor........................................118
Setting the Graph Screen Window Variables............................118
Setting the Graph Format.........................................................119
Displaying the Graph................................................................119
Using Graph Tools in Pol Graphing Mode.....................................119
The Free-Moving Cursor ...........................................................119
Tracing a Polar Equation ..........................................................120
Moving the Trace Cursor to a
q
Value......................................121
Using Zoom Operations............................................................121
The GRAPH MATH Menu..........................................................122
Evaluating an Equation for a Specified
q
..................................122
Drawing on a Polar Graph........................................................122
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-
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Chapter 9: Parametric Graphing 123
Preview: Parametric Graphing ...................................................... 124
Defining a Parametric Graph......................................................... 125
Setting Parametric Graphing Mode..........................................126
The GRAPH Menu.....................................................................126
Displaying the Parametric Equation Editor...............................126
Selecting and Deselecting a Parametric Equation ....................127
Deleting a Parametric Equation................................................ 127
Setting the Graph Screen Window Variables............................ 127
Setting the Graph Format.........................................................128
Displaying the Graph................................................................ 128
Using Graph Tools in Param Graphing Mode................................ 128
The Free-Moving Cursor........................................................... 128
Tracing a Parametric Function..................................................128
Moving the Trace Cursor to a t Value.......................................129
Using Zoom Operations............................................................ 129
The GRAPH MATH Menu.......................................................... 130
Evaluating an Equation for a Specified t ..................................130
Drawing on a Parametric Graph...............................................130
Chapter 10: Differential Equation Graphing 131
Defining a Differential Equation Graph......................................... 132
Setting Differential Equation Graphing Mode .......................... 132
The GRAPH Menu.....................................................................133
Setting the Graph Format.........................................................133
Displaying the Differential Equation Editor ..............................134
Setting the Graph Screen Window Variables............................135
Setting the Initial Conditions....................................................136
Setting the Axes .......................................................................137
Differential Equation Graphing Tips .........................................137
The Built-In Variable fldPic .......................................................138
Displaying the Graph................................................................138
Entering and Solving Differential Equations..................................139
Graphing in SlpFld Format........................................................139
Transforming an Equation into a First-Order System................140
Graphing in DirFld Format........................................................141
Graphing a System of Equations in FldOff Format....................142
Solving a Differential Equation for a Specified Value ...............144
Using Graph Tools in DifEq Graphing Mode .................................144
The Free-Moving Cursor ...........................................................144
Tracing a Differential Equation.................................................144
Moving the Trace Cursor to a t Value.......................................145
Drawing on a Differential Equation Graph ...............................145
Drawing an Equation and Storing Solutions to Lists.................145
Using ZOOM Operations...........................................................147
Drawing Solutions Interactively with EXPLR.............................148
Evaluating Differential Equations for a Specified t ...................150
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Chapter 11: Lists 151
Lists on the TI
-
86 ..........................................................................152
The LIST Menu.......................................................................... 152
The LIST NAMES Menu............................................................. 153
Creating, Storing, and Displaying Lists..........................................153
Entering a List Directly in an Expression................................... 153
Creating a List Name by Storing a List ..................................... 154
Displaying List Elements Stored to a List Name .......................154
Displaying or Using a Single List Element ................................155
Storing a New Value to a List Element.....................................155
Complex List Elements .............................................................156
The List Editor ...............................................................................156
The List Editor Menu ................................................................156
Creating a List Name in the Unnamed Column ........................157
Inserting a List Name into the List Editor .................................157
Displaying and Editing a List Element ......................................158
Deleting Elements from a List ..................................................158
Removing a List from the List Editor ........................................158
Using List Operations....................................................................159
The LIST OPS (Operations) Menu .............................................159
Using Mathematical Functions with Lists .....................................161
Attaching a Formula to a List Name .............................................162
Comparing an Attached List with a Regular List ......................163
Using the List Editor to Attach a Formula ................................163
Using the List Editor With Attached-Formula Lists ...................164
Executing and Displaying Attached Formulas ..........................164
Handling Errors Related to Attached Formulas.........................165
Detaching a Formula from a List Name....................................166
Editing an Element of a Attached Formula List ........................166
Chapter 12: Vectors 167
Vectors on the TI
-
86 .....................................................................168
Creating, Storing, and Displaying Vectors.....................................169
The VECTR (Vector) Menu ........................................................169
The VECTR NAMES Menu.........................................................169
Creating a Vector in the Vector Editor......................................169
The Vector Editor Menu............................................................170
Creating a Vector on the Home Screen.....................................170
Creating a Complex Vector.......................................................171
Displaying a Vector...................................................................171
Using a Vector in an Expression ...............................................172
Editing Vector Dimension and Elements...................................172
The VECTR MATH Menu...........................................................173
The VECTR OPS (Operations) Menu..........................................173
The VECTR CPLX (Complex) Menu ...........................................175
Using Mathematical Functions with Vectors.................................176
Chapter 13: Matrices 177
Matrices on the TI
-
86....................................................................178
Creating, Storing, and Displaying Matrices ...................................178
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-
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The MATRX (Matrix) Menu ...................................................... 178
The MATRX NAMES Menu .......................................................178
Creating a Matrix in the Matrix Editor ..................................... 178
The Matrix Editor Menu ...........................................................179
Creating a Matrix on the Home Screen .................................... 180
Creating a Complex Matrix ......................................................180
Displaying Matrix Elements, Rows, and Submatrices............... 181
Using a Matrix in an Expression............................................... 181
Editing Matrices in the Matrix Editor .......................................182
Editing Matrices on the Home Screen ......................................182
The MATRX MATH Menu ......................................................... 183
The MATRX OPS (Operations) Menu........................................184
The MATRX CPLX (Complex ) Menu......................................... 185
Using Mathematical Functions with Matrices...............................185
Chapter 14: Statistics 187
Statistical Analysis on the TI
-
86.................................................... 188
Setting Up a Statistical Analysis....................................................188
The STAT (Statistics) Menu....................................................... 188
Entering Statistical Data...........................................................189
The LIST NAMES Menu............................................................. 189
The STAT CALC (Calculations) Menu........................................ 189
Automatic Regression Equation Storage..................................191
Results of a Statistical Analysis.....................................................192
The STAT VARS (Statistical Variables) Menu............................192
Plotting Statistical Data.................................................................194
The STAT PLOT Status Screen...................................................194
The STAT PLOT Menu ...............................................................195
Setting Up a Stat Plot ...............................................................195
Turning On and Turning Off a Stat Plot ....................................195
The PLOT TYPE Menu (Selecting a Plot Type)...........................196
Plot Type Characteristics ..........................................................196
The STAT DRAW Menu..................................................................199
Forecasting a Statistical Data Value..............................................199
Chapter 15: Equation Solving 201
Preview: The Equation Solver........................................................202
Entering an Equation in the Equation-Entry Editor........................203
Setting Up the Interactive-Solver Editor........................................204
Entering Variable Values ..........................................................204
Controlling the Solution with Bounds and a Guess ..................204
Editing the Equation.................................................................205
The Solver Menu.......................................................................206
Solving for the Unknown Variable ................................................206
Graphing the Solution...................................................................207
Solver Graph Tools........................................................................207
The Solver ZOOM Menu ...........................................................208
The Simultaneous Equation Solver................................................208
Entering Equations to Solve Simultaneously ............................208
Storing Equation Coefficients and Results to Variables............210
The Polynomial Root-Finder..........................................................211
TI-86 Table of Contents
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Entering and Solving a Polynomial........................................... 211
Storing a Polynomial Coefficient or Root to a Variable ............212
Chapter 16: Programming 213
Writing a Program on the TI-86 ....................................................214
The PRGM Menu ......................................................................214
Creating a Program in the Program Editor ............................... 214
The Program Editor Menu ........................................................ 215
The PRGM I
à
O (Input
à
Output) Menu......................................215
The TI
-
86 Key Code Diagram ...................................................217
The PRGM CTL Menu ...............................................................218
Entering a Command Line........................................................220
Menus and Screens in the Program Editor ...............................220
Running a Program .......................................................................221
Breaking (Interrupting) a Program ........................................... 222
Working with Programs ................................................................ 223
Managing Memory and Deleting a Program ............................223
Editing a Program.....................................................................223
Calling a Program from Another Program................................ 224
Copying a Program to Another Program Name........................ 225
Using and Deleting Variables within a Single Program ............ 225
Running an Assembly Language Program ....................................225
Entering and Storing a String........................................................ 226
The STRNG (String) Menu ........................................................227
Creating a String ......................................................................227
Chapter 17: Memory Management 229
Checking Available Memory .........................................................230
The MEM (Memory) Menu .......................................................230
Checking Memory Usage..........................................................230
Deleting Items from Memory ........................................................231
The MEM DELET (Delete) Menu ...............................................231
Resetting the TI
-
86 .......................................................................232
The MEM RESET (Reset) Menu.................................................232
ClrEnt (Clear Entry)...................................................................232
Chapter 18: The TI
-
86 Communication Link 233
TI
-
86 Linking Options....................................................................234
Linking Two TI
-
86s...................................................................234
Linking a TI
-
86 and a TI
-
85......................................................234
Linking a TI
-
86 and a CBL 2/CBL or CBR System......................234
Linking a TI
-
86 and a PC or Macintosh ....................................235
Downloading Programs from the Internet................................235
Connecting the TI
-
86 to Another Device.......................................235
The LINK Menu.........................................................................236
Selecting Data to Send..................................................................236
The LINK SEND Menu...............................................................236
Initiating a Memory Backup .....................................................237
Selecting Variables to Send ......................................................238
The SEND WIND (Window Variables) Screen............................238
Sending Variables to a TI
-
85 ....................................................239
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-
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The LINK SND85 (Send Data to TI
-
85) Menu ...........................239
Preparing the Receiving Device..................................................... 240
Transmitting Data ......................................................................... 240
Receiving Transmitted Data..........................................................241
Repeating Transmission to Several Devices .............................242
Error Conditions ....................................................................... 242
Insufficient Memory in Receiving Unit......................................242
Chapter 19: Applications 243
Using Math Operations with Matrices .......................................... 244
Finding the Area between Curves.................................................245
The Fundamental Theorem of Calculus......................................... 246
Electrical Circuits...........................................................................248
Program: Taylor Series .................................................................. 250
Characteristic Polynomial and Eigenvalues...................................252
Convergence of the Power Series .................................................254
Reservoir Problem.........................................................................256
Predator-Prey Model.....................................................................258
Program: Sierpinski Triangle .........................................................260
Chapter 20:
A to Z Function and Instruction Reference 261
Quick-Find Locator........................................................................ 262
Alphabetical Listing of Operations................................................266
Appendix 379
TI
-
86 Menu Map...........................................................................380
Handling a Difficulty......................................................................392
Error Conditions ............................................................................393
Equation Operating System (EOS
é
)..............................................397
Implied Multiplication ..............................................................397
Parentheses..............................................................................397
TOL (The Tolerance Editor)............................................................398
Computational Accuracy ...............................................................399
Support and Service Information...................................................400
Product Support........................................................................400
Product Service.........................................................................401
Other TI Products and Services.................................................401
Warranty Information....................................................................402
Customers in the U.S. and Canada Only...................................402
Australia & New Zealand Customers Only................................403
All Customers outside the U.S. and Canada.............................404
Index
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Preparing to Use Your New TI
-
86........................................2
Calculating on the Home Screen.......................................... 3
Plotting Functions on the Graph Screen .............................. 9
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
TI-86 Quick Start
2
Quick Start
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Preparing to Use Your New TI-86
The brief examples in the TI
-
86 Quick Start demonstrate some common TI
-
86 features.
Before you begin, you must install the batteries, turn on the calculator, adjust the contrast,
and reset the memory and the defaults. Chapter 1 has more details on these topics.
Installing the AAA Batteries
Four AAA batteries are included in the TI
-
86 retail package. Remove the batteries from the
package and install them in the battery compartment on the back of the calculator. Arrange
the batteries according to the polarity (+ and
N
) diagram in the battery compartment.
Turning On and Turning Off the TI-86
To turn on the TI
-
86, press
^
, which is in the bottom-left corner of the
keyboard. You should see the entry cursor (
Å
) blinking in the top-left
corner of the screen. If you do not see it, adjust the contrast (see below).
To turn off the calculator, press
-
, and then the key under
OFF
, which is
^
. This guidebook uses brackets (
ã
and
ä
) to express
-
and
1
keystroke combinations. For example, to turn off the TI
-
86, press
-
.
ON
1
0
ST
=
U
Y
RCL
BASE
CHAR
O
OFF
Adjusting the Contrast
Press and release the yellow - key.
Press and hold $ or # (above or below the half-shaded circle).
To darken the screen contrast, press and hold $.
To lighten the screen contrast, press and hold #.
EXIT
x-VAR
MORE
DEL
2nd
ALPHA
x
QUIT
alpha
LINK
INS
MODE
After about four minutes of
inactivity, the TI
-
86 turns off
automatically.
If you release
$
or
#
while
adjusting the contrast, you
must press
-
again to
continue the adjustment.
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Resetting All Memory and Defaults
To reset all memory and defaults, press
-
(
&
)
. The messages
Mem cleared
and
Defaults set
are displayed on the home screen, confirming that all memory and defaults are
reset. You may need to adjust the contrast after memory and default reset.
Calculating on the Home Screen
To replicate the screens shown in the Quick Start activities, reset all memory and defaults
once before you begin. Before doing an activity, press
:
to clear the screen (except
before the entry retrieval and integer-part examples). Otherwise, the screens your TI
-
86
shows may differ from the screens pictured next to the activities.
Calculating the Sine of a Number
Enter the sine function. (
:
)
=
Enter a value. You can enter an expression,
which is evaluated when you press
b
.
D
-
~
F
4
E
Evaluate the problem. The evaluation of the
expression sine(
4) is displayed.
b
Storing the Last Answer to a Variable
Paste the store symbol (
) to the screen.
Since a value must precede
, but you did
not enter a value, the TI
-
86 automatically
pasted
Ans
before
. (
continued
)
(
:
)
X
To express
-
and
1
keystroke combinations, this
guidebook places brackets
(
ã
and
ä
)
around the word
above the key to press.
The TI
-
86 on-screen division
symbol is a forward slash
(
à
)
, as in a fraction.
Following evaluation, the
entry cursor automatically
moves to the next line, ready
for a new entry.
When the TI
-
86 evaluates an
expression, it automatically
stores the answer to the built-
in variable
Ans
, replacing
any previous value.
4
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Enter the variable name to which you want
to store the last answer. ALPHA-lock is on.
ã
V
ä
Store the last answer to the variable. The
stored value is displayed on the next line.
b
Using a Variable in an Expression
Enter the variable, and then square it. (:)
1
ã
V
ä
I
Evaluate. The value stored to the variable
V
is squared and displayed.
b
Editing an Expression
Enter the expression
(25+14)(4
N
3.2)
.(:)
D
25
\
14
E
D
4
T
3
`
2
E
Change
3.2
to
2.3
. ! ! ! !
2
"
3
Move the cursor to the beginning of the
expression and insert a value. The insert
cursor blinks between
3
and
25
.
- ! - p
3
Evaluate. The result is displayed. b
When ALPHA-lock is on and
you press a key, the letters
printed in blue above the
keys are pasted to the
screen. In the example, press
Z
to enter a
V
.
You need not move the
cursor to the end of the line
to evaluate the expression.
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Displaying a Complex Number as a Result
Enter the natural log function. (:) B
Enter a negative number. D a
2
E
Evaluate. The result is displayed as a
complex number.
b (press "
to display more)
Using a List with a Function
Enter the exponential function. (:) -
Display the
LIST
menu, and then select the
open brace (
{
) from the
LIST
menu.
On the TI
-
86,
{
specifies the beginning of a
list.
-
&
LIST
menu
Enter the list elements. Separate each
element from the next with a comma.
5
P
10
P
15
Select the close brace (
}
) from the
LIST
menu to specify the end of the list.
Evaluate. The results of the constant
e
raised to the 5th, 10th, and 15th powers are
displayed as list elements.
'
b (press "
to display more)
a
negates a value, as in
L
2
.
T
subtracts, as in
5
N
2=3
.
An ellipsis (...) indicates that
the result continues beyond
the screen.
6
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Displaying the Integer Part of Real Numbers in a List
Display the
MATH
menu. (The
MATH
menu
automatically replaces the
LIST
menu from
the last activity.)
- Œ
MATH
menu
Select
NUM
to display the
MATH
NUM
menu. The
MATH
menu shifts up.
&
MATH NUM
menu
Select the
iPart
(integer part) function from
the
MATH
NUM
menu.
iPart
is pasted to the
screen. (The previous entry was left on the
screen to illustrate the effect of
iPart
on the
previous answer.)
'
Paste
Ans
to the cursor location. (The
result list from the previous activity is
stored to
Ans
.)
-
¡
Display the integer part of the result list
elements from the previous activity.
b
Removing (Exiting) a Menu
In the previous example, the
MATH
menu and the
MATH
NUM
menu are displayed (- Œ &).
Remove the
MATH
NUM
menu from the screen. .
Remove the
MATH
menu from the screen. .
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Finding the Square Root
Paste the square root function to the screen. (:) - ˆ
Enter a value for which you want to find the
square root.
144
Evaluate the expression. The square root of
144
is displayed.
b
Calculating Derivatives
Display the
CALC
menu, and then select
der1
.
(:)
-
(
CALC
menu
Enter an expression (
x
2
) with respect to a
variable (
x
) at a given point (
8
).
2 I P 2
P
8
E
Evaluate. The first derivative of
x
2
with
respect to
x
at
8
is displayed.
b
8
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Retrieving, Editing, and Re-evaluating the Previous Entry
Retrieve the last entry from the previous
example. (The last activity was not cleared.)
- ¢
Edit the retrieved entry. ! !
3
Evaluate. The first derivative of
x
2
with
respect to
x
at
3
is displayed.
b
Converting Degrees Fahrenheit to Degrees Celsius
Display the
CONV
menu. (:) -
Display the
CONV
TEMP
menu. The
CONV
menu shifts up and
TEMP
is highlighted.
*
Enter the known measurement. If the
measurement is negative, use parentheses.
In this example, if you omit parentheses,
the TI
-
86 converts 4
¡
F to about
L
15.5
¡
C,
which it then negates (changes the sign
of), returning a positive 15.5
¡
C.
D a
4
E
Select
¡
F
to designate Fahrenheit as the
known measurement unit.
¡
F
and the
conversion symbol (
4
) are displayed after
the measurement. (
continued
)
'
When you press
b
, the
TI
-
86 stores the expression
or instruction you entered to
the built-in memory storage
area called
ENTRY
.
When expressing a
measurement for a
conversion, you do not enter
a unit symbol manually. For
example, you need not enter
¡
to designate degrees.
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Select
¡
C
to designate Celsius as the unit
to which you want to convert.
&
Convert. The
¡
C equivalent of
L
4
¡
F is
displayed.
b
Storing an Unevaluated Expression to an Equation Variable
Enter the built-in equation variable
y1
.(:) - n
ã
Y
ä
1
Enter the equals sign (=). 1
ã
=
ä
Enter an expression in terms of
x
.
Store the expression.
5
D = 2 E
b
The next section shows how to graph the functions
y1=5(sin x)
and
y2=5(cos x)
.
Plotting Functions on the Graph Screen
The TI
-
86 plots four types of functions on the graph screen. To plot a graph, you must store
an unevaluated expression to a built-in equation variable.
Each activity in this section builds upon the activity that precedes it. You must start here
and perform the activities in the sequence in which they are presented. The first activity in
this section assumes you are continuing from the last activity in the previous section.
Displaying and Entering Functions in the Equation Editor
Display the
GRAPH
menu. (
continued
) 6
When storing to an equation
variable using
=
, enter the
equation variable first, then
=
,
and then the unevaluated
expression. This is the
opposite from the order for
storing to most other
variables on the TI
-
86.
10
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Select
y(x)=
from the
GRAPH
menu to
display the equation editor.
5(sin x)
is the
unevaluated expression stored to
y1
in the
previous activity. The equation editor
menu is displayed as the lower menu.
&
equation
editor menu
Move the cursor down. The
y2=
prompt is
displayed.
#
Enter the expression
5(cos x)
at the
y2=
prompt. Notice that the equals sign (
=
) of
y2
is highlighted after you enter
5
. Also,
the equals sign of
y1
is highlighted. This
indicates that both equations are selected
to be graphed (Chapter 5).
5
D > 2 E
Changing the Graph Style of a Function
In the equation editor, the icon to the left of each equation specifies the style in which the
graph of that equation appears when you plot it on the graph screen.
Move the cursor to
y1
. $
Display the next menu group of the equation
editor menu. (
4
at the end of a menu group
indicates that the menu has more items.)
/
Select
STYLE
from the equation editor
menu to set ¼ (thick) graph style for
y1
.
(
graph style icons
In the equation editor, you
must express each equation
in terms of the independent
variable
x
(in
Func
graphing
mode only; Chapter 5).
To display up to seven graph
styles, depending on the
graphing mode, repeat
(
.
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Plotting a Function on the Graph Screen
Select
GRAPH
from the
GRAPH
menu to
plot the graph on the graph screen. The x-
and y-axes and
GRAPH
menu are
displayed. Then each selected graph is
plotted in the order in which it is listed in
the equation editor.
- i
free-moving cursor
When the graph is plotted, you can move
the free-moving cursor (
+
) around the
graph screen. The cursor coordinates are
displayed at the bottom of the graph.
" # ! $
Tracing a Function
Select
TRACE
from the
GRAPH
menu to
activate the trace cursor, with which you
can trace along the graph of any selected
function. The number of the current
function (the
1
in
y1
) is displayed in the
top-right corner.
)
trace cursor
Move the trace cursor from the function
y1
to the function
y2
. The
1
in the top-right
corner changes to
2
; the
y
value changes to
the value of
y2
at
x=0
. (
continued
)
$
12
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Trace the function
y2
. As you trace, the
displayed
y
value is the solution for
5(cos x)
at the current
x
value, which also
is displayed on the screen.
" and !
Evaluating y for a Specific x Value (During a Trace)
Enter a real number (or an expression that
resolves to a real number) that is within
the dimensions of the current graph
screen. When you enter the first character,
the
x=
prompt is displayed.
6
Evaluate
y2
at
x=6
. The trace cursor
moves directly to the solution. The
y
value,
or solution of the equation at
x
, is
displayed on the screen.
b
Changing a Window Variable Value
Display the
GRAPH
menu. 6
Select
WIND
from the
GRAPH
menu to
display the window editor.
(
continued
)
'
The window variables values
determine the dimensions of
the graph screen.
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Change the value stored in the
xMin
window variable to
0
.
0
Plot the graph on the redefined graph
screen. Since
xMin=0
, only the first and
fourth quadrants of the graph plane are
displayed.
*
Deselecting a Function
Select
y(x)=
from the
GRAPH
menu to
display the equation editor and equation
editor menu. The
GRAPH
menu shifts up
and
y(x)=
is highlighted.
&
Select
SELCT
from the equation editor
menu to deselect the function
y1=
. The
equals sign is no longer highlighted.
*
Plot the graph on the graph screen. Since
you deselected
y1
, the TI
-
86 only plots
y2
.
To select a function in the equation editor,
repeat these steps. (
SELCT
both selects
and deselects functions.)
- i
14
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Zooming In on a Portion of the Graph Screen
Select
ZOOM
to display the
GRAPH
ZOOM
menu. The
GRAPH
menu shifts up and
ZOOM
is highlighted.
(
Select
BOX
from the
GRAPH
ZOOM
menu
to activate the zoom-box cursor.
Move the zoom-box cursor to a point that is
to be a corner of the redefined graph screen,
and then mark the point with a small square.
&
" # ! $
b
Move the cursor away from the small
square to a point that is to be the opposite
corner of the redefined graph screen. As
you move the cursor, a rectangle is drawn
on the graph.
" # ! $
Zoom in on the graph. The window
variables change automatically to the
specifications of the zoom box.
Clear the menus from the graph screen.
b
:
01OPER.DOC TI-86, Chap 1, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 2:59 PM Page 15 of 22
Installing or Replacing Batteries ........................................ 16
Turning On and Turning Off the TI
-
86 ............................... 17
Adjusting the Display Contrast .......................................... 17
The Home Screen...............................................................18
Entering Numbers..............................................................19
Entering Other Characters .................................................20
Entering Expressions and Instructions ............................... 24
Diagnosing an Error ........................................................... 27
Reusing Previous Entries and the Last Answer .................. 28
Using TI
-
86 Menus ............................................................ 31
Viewing and Changing Modes........................................... 34
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Operating
the TI-86
1
16
Chapter 1: Operating the TI
-
86
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Installing or Replacing Batteries
Your new TI
-
86 includes four AAA alkaline batteries. You must install them before you can
turn on the calculator. A lithium backup battery is installed in the calculator already.
If the calculator is on, turn it off (press
-
) to avoid loss of information stored in memory.
Slide the protective cover over the keyboard.
Holding the calculator upright, push down on the battery cover latch, and then remove the cover.
Remove all four old batteries.
Install four new AAA alkaline batteries, arranged according to the polarity (+ and
N
) diagram
inside the battery compartment.
Replace the battery cover by inserting the two prongs into the two slots at the bottom of the
battery compartment, and then push the cover until the latch snaps closed.
When to Replace Batteries
When the AAA batteries are low, a low-battery message is
displayed as you turn on the calculator. Generally, the
calculator will continue to operate for one or two weeks
after the low-battery message is first displayed.
Eventually, the TI
-
86 will turn off automatically and will
not operate until you replace the AAA batteries.
The lithium backup battery is inside the battery compartment, above the AAA batteries. It
retains all memory when the AAA batteries are low or have been removed. To avoid loss of
data, do not remove the lithium battery unless four fresh AAA batteries are installed.
Replace the lithium backup battery about every three or four years.
To express
-
and
1
keystroke combinations, this
guidebook places brackets
(
ã
and
ä
)
around the word
above the key to press.
Do not remove the lithium
backup battery unless four
fresh AAA batteries are in
place.
Properly dispose of the old
batteries.
If you do not use your TI
-
86
frequently, the AAA batteries
could last more than two
weeks after the first low-
battery message.
Chapter 1: Operating the TI
-
86
17
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To replace the lithium backup battery, remove the battery cover and unscrew the tiny
screw holding the
BACK UP BATTERY
cover in place. Install a new
CR1616
or
CR1620
battery
according to the polarity (+ and
N
) diagram on the cover. Replace the cover and screw.
Turning On and Turning Off the TI-86
To turn on the TI
-
86, press
^
.
If you
previously had turned off the calculator by
pressing
-
, the TI
-
86 clears any errors and
displays the home screen as it was last displayed.
If Automatic Power Down
TM
(APD
TM
) previously had
turned off the calculator, the TI
-
86 will return as you
left it, including the display, cursor, and any error.
ON
1
0
2
3
65
4
ST
,
(
(
=
S
U
Y
Z
VW
RCL
CONS
STRNG
BASE TES MEM
:
ANS
CHAR
O
OFF
CONV
T
PRQ
To turn off the TI
-
86 manually, press
-
. All settings and memory contents are
retained by the Constant Memory
TM
feature. Any error condition is cleared.
APD turns off the TI
-
86 automatically after about four minutes of non-use to extend battery life.
Adjusting the Display Contrast
Press and release the yellow
-
key.
Press and hold
$
or
#
(above or below the half-shaded circle).
To darken the screen contrast, press and hold
$
.
To lighten the screen contrast, press and hold
#
.
EXIT
x-VAR
MORE
DEL
2nd
ALPHA
x
QUIT
alpha
LINK
INS
MODE
Properly dispose of the old
battery.
If you release
$
or
#
while
adjusting the contrast, you
must press
-
again to
continue the adjustment.
18
Chapter 1: Operating the TI
-
86
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You can adjust the display contrast anytime to suit your viewing angle and lighting
conditions. As you adjust, a number from
0
(lightest) to
9
(darkest) in the top-right corner
indicates the current contrast setting. The number is not visible when the contrast is
extremely light or dark.
As the batteries weaken over time, the actual contrast level of each number shifts. For
example, say you set the contrast to
3
with fresh batteries. As the batteries weaken, you will
need to set the contrast to
4
, then
5
, then
6
, and so on, to retain the original contrast level.
However, you need not replace the batteries until the low-battery message is displayed.
The Home Screen
When you first turn on your TI
-
86, the home screen is displayed. Initially, the home screen
is a blank screen, except for the entry cursor (
Å
) in the top-left corner. If you do not see
the cursor, press
-
, and then press and hold
#
or
$
to adjust the contrast (page 17).
On the home screen, you can enter and evaluate expressions, and view the results. You also
can execute instructions, store and recall variable values, and set up graphs and editors.
To return to the home screen from any other screen, press
-
l
.
Displaying Entries and Answers
The home screen displays up to eight lines with a maximum of 21 characters per line. If an
expression or series of instructions exceeds 21 characters and spaces, it automatically
continues on the next line.
After all eight lines are full, text scrolls off the top of the display. You can press
$
to scroll
up the home screen, only as far as the first character in the current entry. To retrieve, edit,
and re-execute previous entries, use
-
¢
(page 28).
The TI
-
86 has 40 contrast
settings, so each number
0
through
9
represents four
settings.
You need not clear the home
screen to begin a new entry.
Chapter 1: Operating the TI
-
86
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When an entry is executed on the home screen, the
answer is displayed on the right side of the next line.
When you execute an instruction,
Done
is typically
displayed on the right side of the next line.
If an answer is too long to display on the screen, an
ellipsis (...) is displayed, initially to the right. To view
more of the answer, press
"
. When you do, an ellipsis
is displayed to the left. To scroll back, press
!
.
Entry
Answer
Entry
Answer
Entering Numbers
A symbol or abbreviation of each key’s primary function is printed in white on the key. For
example, when you press
\
, a plus sign is pasted to the cursor location. This guidebook
describes number-entry keystrokes as
1
,
2
,
3
, and so on, instead of
Y
Z
[
.
Entering Negative Numbers
To enter a negative number, press
a
(the negate key), and then press the appropriate
number keys. For example, to enter
L
5
, press
a
5
. Do not attempt to express a negative
number using
T
(the subtract key).
a
and
T
are two different keys with different uses.
The order in which the TI
-
86 evaluates negation and other functions within an expression is
governed by the Equation Operating System
è
(Appendix). For example, the result of
L
4
2
is
L
16
, while the result of
(
L
4)
2
is
16
. If you are unsure about the order of evaluation, use
D
and
E
to clarify the intended use of the negation symbol.
The mode settings control th
e
way the TI
-
86 interprets
expressions and displays
answers (page 34).
The TI
-
86 on-screen division
symbol is a forward slash
(
à
)
, as in a fraction.
Always use parentheses to
clarify negation when you us
e
conversion instructions
(Chapter 4).
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Using Scientific or Engineering Notation
Enter the mantissa (part of the number that precedes
the exponent). This value can be an expression.
D
19
F
2
E
Paste
E
to the cursor location. C
If the exponent is negative, paste
L
to the cursor location.
Then enter a one-, two-, or three-digit exponent.
a
2
Evaluate the expression. b
When you include scientific- or engineering-notation numbers in an expression, the TI
-
86
does not necessarily display answers in scientific or engineering notation. The mode
settings (page 34) and the size of the number determine the notation of displayed answers.
Entering Complex Numbers
On the TI
-
86, the complex number a+bi is entered as
(
a
,
b
)
in rectangular complex-number form or as
(
r
q
)
in polar
complex-number form. For more information about
complex numbers, read Chapter 4.
Entering Other Characters
EXIT
x-VAR
MORE
DEL
2nd
ALPHA
x
QUIT
alpha
LINK
INS
MODE
In scientific notation only, one
digit precedes the decimal.
In engineering notation, one,
two, or three digits precede
the decimal and the power of
10 exponent is a multiple of 3.
This is the 2nd key
This is the ALPHA key
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The 2nd Key
The
-
key is yellow. When you press
-
, the cursor
becomes
Æ
(the 2nd cursor). When you press the next key,
the yellow character, abbreviation, or word printed above
that key is activated, instead of the key’s primary function.
-
š
returns
the
STAT
menu
X
STAT
The ALPHA Key
The
1
key is blue. When you press
1
, the cursor
becomes
³
(the uppercase ALPHA cursor). When you
press the next key, the blue uppercase character printed
above that key is pasted to the cursor location.
X
STAT
1
ã
X
ä
returns an
X
When you press
-
n
, the cursor becomes
Ï
(the
lowercase alpha cursor). When you press the next key, the
lowercase version of the blue character is pasted to the
cursor location.
X
STAT
-
n
ã
X
ä
returns an
x
ALPHA-lock and alpha-lock
To enter more than one uppercase or lowercase alpha character consecutively, set ALPHA-
lock (for uppercase letters) or alpha-lock (for lowercase letters).
To set ALPHA-lock when the entry cursor is displayed, press
1
1
.
To cancel ALPHA-lock, press
1
.
To switch from ALPHA-lock to alpha-lock, press
-
n
.
To set alpha-lock when the entry cursor is displayed, press
-
n
1
.
To cancel alpha-lock, press
1
1
.
To enter a space within text,
press
1
¤
. Spaces are
not valid within variable
names.
For convenience, you can
press
2
instead of
-
n
ã
x
ä
to enter the
commonly used
x
variable.
The
Name=
prompt and store
symbol
(
)
set ALPHA-lock
automatically.
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To switch from alpha-lock to ALPHA-lock, press
1
.
You can use
-
when ALPHA-lock or alpha-lock is on. Also, if you press a key that has no
blue character above it, such as
6
,
3
, or
!
, the key’s primary function still applies.
Common Cursors
Entry
Å
Enters a character at the cursor, overwriting any existing character
Insert
__
Inserts a character at the cursor location and shifts remaining characters right
Second
Æ
Enters a 2nd character or executes a 2nd operation (yellow on the keyboard)
A
LPHA
³
Enters an uppercase ALPHA character (blue on the keyboard)
alpha
Ï
Enters the lowercase version of an ALPHA character (blue on the keyboard)
Full
Ä
Accepts no data; maximum characters are entered at a prompt or memory is full
If you press
1
after
-
p
, the cursor becomes an underlined
A
(
A
).
If you press
-
1
after
-
p
, the cursor becomes an underlined
a
(
a
).
If you press
-
after
-
p
, the insert cursor becomes an underlined
#
(
#
).
In most cases, the
appearance of the cursor
indicates what will happen
when you press the next key.
Graphs and editors
sometimes use additional
cursors, which are described
in other chapters.
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Cursor Direction Keys
!
moves cursor left
-
!
moves cursor to beginning of entry
-
# scrolls/
moves cursor down
- #
lightens screen contrast
"
moves cursor right
- "
moves cursor to end of entry
-
$
scrolls/moves cursor up
-
$
darkens screen contrast
If you hold down
"
,
#
,
!
, or
$
, the cursor continues to move.
Inserting, Deleting, and Clearing Characters
-
p
Changes the cursor to the insert cursor (
__
); inserts characters at the insert cursor and
shifts remaining characters right; to cancel insert, press
-
p
or press
"
,
#
,
!
, or
$
3
Deletes a character at the cursor; to continue deleting to the right, hold down
3
:
Clears the current entry on the home screen;
:
:
clears the entire home screen
The entry cursor
(
Å
)
overwrites characters.
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Entering Expressions and Instructions
Entering an Expression
An expression is any combination of numbers and variables that serve as arguments for one
or more functions. On the TI
-
86, you typically enter an expression in the same order as you
would write it on paper. For example,
p
r
2
,
5 tan xStat
, and
40((
L
5+3)
N
(2+3))
are expressions.
You can use an expression on the home screen to
calculate an answer.
In most places where a value is required, you can use an
expression to enter the value.
For example, enter an expression as a window variable value
(Chapter 5). When you press
#
,
$
,
b
, or
.
, the TI
-
86
evaluates the expression and replaces it with the result.
To enter an expression, you enter numbers, variables, and functions from the keyboard and
menus (page 31). When you press
b
, the expression is evaluated (regardless of the cursor
location) according to EOS order-of-evaluation rules (Appendix), and the answer is displayed.
To enter the expression 3.76 ÷ (
L
7.9 +
5) + 2 log 45 and
then evaluate it, you would press these keys:
3
`
76
F
D
a
7
`
9
\
-
ˆ
5
E
\
2
<
45
b
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Using Functions in Expressions
A function returns a value. Some examples of functions are
÷
,
L
,
+
,
, and
log
. To use
functions, you usually must enter one or more valid arguments.
When this guidebook describes the syntax of a function or instruction, each argument is in
italics. For example:
sin
angle
. Press
=
to enter
sin
, and then enter a valid
angle
measurement (or an expression that resolves to
angle
). For functions or instructions with
more than one argument, you must separate each argument from the other with a comma.
Some functions require the arguments to be in parentheses. When you are unsure of the
evaluation order, use parentheses to clarify a function’s place within an expression.
Using an Instruction
An instruction initiates an action. For example,
ClDrw
is an instruction that, when executed,
clears all drawn elements from a graph. You cannot use an instruction in an expression.
Generally, the first letter of each instruction name is uppercase on the TI
-
86. Some
instructions take more than one argument, as indicated by an open parenthesis (
(
) at the
end of the name. For example,
Circl(
requires three arguments,
Circl(
x
,
y
,
radius
)
.
Entering Functions, Instructions, and Operators
You can enter a function, instruction, or operator in any of three ways (
log 45
, for example).
Paste it to the cursor location from the keyboard or a menu (
<
45
).
Paste it to the cursor location from the
CATALOG
(
-
w
&
ã
L
ä
&
&
b
45
).
Enter it letter by letter (
-
n
1
ã
L
ä
ã
O
ä
ã
G
ä
¤
1
1
45
).
As you can see in the example, using the built-in function or instruction typically is easier.
In this guidebook, optional
arguments are shown in
brackets
(
ã
and
ä
)
. Do not
include these brackets when
you enter the arguments.
The A to Z Reference
describes all TI
-
86 functions
and instructions, including
their required and optional
arguments.
In the
CATALOG
, to move to
the first item beginning with a
letter, press that letter (as in
ã
L
ä
in the example).
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When you select a function, instruction, or operator, a symbol comprising one or more
characters is pasted to the cursor location. Once the symbol is pasted to the cursor
location, you can edit individual characters.
For example, assume that you pressed
-
w
/
/
*
&
&
b
to paste
yMin
to the cursor location as part of an expression. Then you realized you wanted
xMin
.
Instead of pressing nine keys to select
xMin
, you can simply press
!
!
!
!
2
.
Entering Consecutive Entries
To enter two or more expressions or instructions
consecutively, separate each from the next with a colon
(
-
). When you press
b
, the TI
-
86 executes
each entry from left to right and displays the result of the last expression or instruction. The
entire group entry is stored in last entry (page 28).
The Busy Indicator
When the TI
-
86 is calculating or graphing, a moving vertical line is displayed as the busy
indicator in the top-right corner of the screen. When you pause a graph or a program, the
busy indicator is replaced by the pause indicator, a moving vertical dotted line.
Interrupting a Calculation or Graph
To interrupt a calculation or graph in progress, press
^
. When you interrupt a calculation,
the
ERROR 06 BREAK
message and menu are displayed.
To return to the home screen, select
QUIT
(press
*
).
To go to the beginning of the expression, select
GOTO
(press
&
). Press
b
to
recalculate the expression.
In the example, the
symbol
indicates that the value
before it is to be stored to the
variable after it (Chapter 2).
To paste
to the screen,
press
X
.
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When you interrupt a graph, a partial graph and the
GRAPH
menu are displayed.
To return to the home screen, press
:
:
or any non-graphing key.
To restart graphing, select an instruction that displays the graph.
Diagnosing an Error
When the TI
-
86 detects an error, it returns an error
message, such as
ERROR 04 DOMAIN
or
ERROR 07 SYNTAX
.
The Appendix describes each error type and possible
reasons for the error.
If you select
QUIT
(or press
-
l
or
:
:
), the home screen is displayed.
If you select
GOTO
, the previous screen is displayed with the cursor on or near the error.
Correcting an Error
Note the error type (
ERROR ## errorType
).
Select
GOTO
, if available. The previous screen is displayed with the cursor on or near the error.
Determine the cause for the error. If you cannot, refer to the Appendix for possible causes.
Correct the error and continue.
Chapter 5: Function Graphin
g
introduces graphing.
If a syntax error occurs within
a stored equation during
program execution, select
GOTO
to return to the
equation editor, not to the
program (Chapter 5).
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Reusing Previous Entries and the Last Answer
Retrieving the Last Entry
When you press
b
on the home screen to evaluate an expression or to execute an
instruction, the entire expression or instruction is placed in a storage area called
ENTRY
(last entry). When you turn off the TI
-
86,
ENTRY
is retained in memory.
To retrieve the last entry, press
-
¢
. The current
line is cleared and the entry is pasted to the line.
Retrieving and Editing the Last Entry
On the home screen, retrieve the previous
entry.
Edit the retrieved entry.
Re-execute the edited entry.
-
¢
!
!
!
!
!
32
b
Retrieving Previous Entries
The TI
-
86 retains as many previous entries as possible in
ENTRY
, up to a capacity of 128
bytes. To scroll from the newest to the older previous entries stored to
ENTRY
, repeat
-
¢
. If you press
-
¢
after displaying the oldest stored entry, the newest
stored entry is displayed again; continuing to press
-
¢
repeats the order.
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-
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Retrieving Multiple Entries
To store two or more expressions or instructions together to
ENTRY
, enter them on one
line, separating each from the other with a colon, and then press
b
. Upon execution,
the entire group is stored in
ENTRY
. The example below shows one of many ways you can
manipulate this feature to avoid tedious manual re-entry.
Use trial and error to find the radius
of a circle with an area of 200 square
centimeters. Store
8
to
r
as your first
guess, then execute
p
r
2
.
8
X
-
n
ã
R
ä
-
[
:
]
-
~
ã
R
ä
1
1
I
b
Retrieve
8r:
p
r
2
and insert
7.958
as a
new guess. Continue guessing to
approach the answer of
200
.
-
¢
-
!
7
-
p
`
958
b
Clearing the ENTRY Storage Area
To clear all data from the
ENTRY
storage area, begin on a blank line on the home screen,
select
ClrEnt
from the
MEM
menu (press
-
*
), and then press
b
.
Retrieving the Last Answer
When an expression is evaluated successfully on the home screen or in a program, the TI
-
86
stores the answer to a built-in variable called
Ans
(last answer).
Ans
may be a real or
complex number, list, vector, matrix, or string. When you turn off the TI
-
86, the value in
Ans
is retained in memory.
Consecutively entered entries
separated by colons (page 26
)
are stored as one entry.
The formula for finding the
area of a circle is
A=
p
r
2
.
The equation solver (Chapter
15) is another tool with which
you can perform this task.
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To copy the variable name
Ans
to the cursor location, press
-
¡
. You can use the
variable
Ans
anywhere that the value stored to it is valid. When the expression is evaluated,
the TI
-
86 calculates the result using the value stored in
Ans
.
Calculate the area of a garden plot
1.7
meters
by
4.2
meters.
Calculate the yield per square meter if the plot
produces a total of
147
tomatoes.
1
`
7
M
4
`
2
b
147
F
-
¡
b
Using Ans Preceding a Function
Previous answers are stored to
Ans
. If you begin an expression by entering a function that
requires a preceding argument, the TI
-
86 automatically enters
Ans
as the argument.
Enter and execute an expression.
Enter a function without an argument.
Ans
is
pasted to the screen, followed by the function.
5
F
2
b
M
9
`
9
b
Storing Results to a Variable
Calculate the area of a circle with radius
5
meters.
Calculate the volume of a cylinder of radius
5
meters and height
3.3
meters.
Store the result to the variable
V
.
-
~
5
I
b
M
3
`
3
b
X
ã
V
ä
b
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Using TI-86 Menus
The symbols for many TI
-
86 features are found in menus instead of on the TI
-
86 keyboard.
Displaying a Menu
The way to display a particular menu depends on the menu’s location on the TI
-
86.
Menu-Displaying Method Example
Press a key that has a menu name on it
6
displays the
GRAPH
menu
Press
-
and then a 2nd-key menu name
-
Œ
displays the
MATH
menu
Select a menu name from another menu
-
Œ
&
displays the
MATH
NUM
menu
Select an editor or selection screen
-
)
displays the list editor menu with the list editor
A
ccidentally commit an error
1
X
b
displays the error menu
When you display a menu, a menu group of one to five items is displayed on the bottom of the
screen. If the more symbol (
4
) is displayed after the fifth item in a menu group, the menu
continues for at least one more menu group. To view the next menu group, press
/
. The
last menu group of one to five items does not have a
4
symbol.
For example, press
-
Œ
to display
the
MATH
menu.
When you see
4
here...
...press
/
to display
the next menu group.
From the last menu group, press
/
again to return to the first menu group.
Some TI
-
86 menus have as
many as 25 items.
"
,
#
,
!
, and
$
do not
work on menus.
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The Menu Keys
-
upper menu keys
M1 M2 M3 M4 M5
lower menu keys
&
'
(
)
*
-
l
clears all menus
QUIT
-
e
through
i
selects
-
.
/
/
scrolls lower menu groups
upper menu items
.
removes the lower menu
Selecting a Menu Item
When you display a menu, one to five items are displayed.
To select a menu item, press the menu selection key directly
below the item. For example, in the
MATH
menu to the right,
press & to select
NUM
, press ' to select
PROB
, and so on.
&
'
(
)
*
When you select a menu item that displays another menu, the first menu moves up one line
on the screen to make room for the new menu. All items on the original menu are displayed
in reverse type, except the item you selected.
When you select
NUM
...
...the
MATH
menu moves up
and the
MATH
NUM
menu is displayed.
To remove the
MATH
NUM
menu and
move the
MATH
menu down, press
.
.
The Appendix Menu Map
shows every TI
-
86 menu.
Typically, a TI
-
86 menu item
is five characters long or less.
/
only scrolls the lower
menu; it does not scroll the
upper menu.
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-
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To select an item from the upper menu, press
-
and the appropriate key
e
through
i
.
To select
PROB
from the upper menu, press
-
f
.
To select
iPart
from the lower menu, press
'
.
When an editor menu is displayed as the upper menu, and you select an item from the lower
menu that displays yet another menu, the editor menu remains as the upper menu.
When you select
NUM
from the lower menu... The
MATH
menu disappears.
...the equation editor
menu remains
and the
MATH
NUM
menu is displayed.
Upper: equation editor menu
Lower:
MATH
menu
Upper: equation editor menu
Lower:
MATH
NUM
menu
Exiting (Removing) a Menu
To remove the lower menu from the screen, press
.
.
When you press
.
...
...the
MATH
NUM
menu disappears
and the
MATH
menu moves down.
Press
.
again, and
the
MATH
menu disappears.
Upper:
MATH
menu
Lower:
MATH
NUM
menu Lower:
MATH
menu No menu
To remove a menu from the
bottom of a graph screen,
press
:
after plotting th
e
graph (Chapter 5).
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Viewing and Changing Modes
To display the mode settings, press
-
m
. The current
settings are highlighted. Mode settings control how the
TI
-
86 displays and interprets numbers and graphs. The
Constant Memory feature retains current mode settings
when the TI
-
86 is turned off. All numbers, including
elements of matrices and lists, are displayed according to
the mode settings.
Changing a Mode Setting
Move the cursor to the line of the setting that you
want to change (decimal setting in the example).
Move the cursor to the setting you want (2 decimal
places).
Execute the change.
#
"
"
"
b
Notation Modes
Normal
Displays results with digits to the left and right of the decimal (as in
123456.7
)
Sci
(scientific) Displays results in two parts: significant digits (with one digit to the left of
the decimal) are displayed to the left of
E
and the appropriate power of 10 is displayed
to the right of
E
(as in
1.234567E5
)
Eng
(engineering) Displays results in two parts: significant digits (with one, two, or three
digits to the left of the decimal) are displayed to the left of
E
and the appropriate power
of 10 (which is always a multiple of 3) is displayed to the right of
E
(as in
123.4567E3
)
In the screen to the right, the
default mode settings are
highlighted along the left side
of the screen.
This example changes the
decimal mode setting to 2, as
in U.S. dollars and cents.
In
Normal
notation, if the
answer is more than 12 digits
or the absolute value of the
answer < .001, it is displayed
in scientific notation.
Notation modes do not affect
how you enter numbers.
Chapter 1: Operating the TI
-
86
35
01OPER.DOC TI-86, Chap 1, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 2:59 PM Page 35 of 2201OPER.DOC TI-86, Chap 1, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 2:59 PM Page 35 of 22
Decimal Modes
Float
(floating) Displays results up to 12 digits, plus any sign and the floating decimal point
(fixed) (
012345678901
; each number is a setting) Displays results with the specified number of
digits to the right of the decimal point (rounds answers to the specified decimal place);
the second
0
sets 10; the second
1
sets 11
An
g
le Modes
Radian
Interprets angle values as radians; displays answers in radians
Degree
Interprets angle values as degrees; displays answers in degrees
Complex Number Modes
RectC
(rectangular complex mode) Displays complex-number results as
(real,imaginary)
PolarC
(polar complex mode) Displays complex-number results as
(magnitude
±
angle)
Graphin
g
Modes
Func
(function graphing) Plots functions where
y
is a function of
x
Pol
(polar graphing) Plots functions where
r
is a function of
q
Param
(parametric graphing) Plots relations where
x
and
y
are functions of
t
DifEq
(differential equation graphing) Plots differential equations in terms of
t
Number Base Modes
Dec
(decimal number base) Interprets and displays numbers as decimal (base 10)
Bin
(binary number base) Interprets numbers as binary (base 2); displays
Ü
suffix with answers
Oct
(octal number base) Interprets numbers as octal (base 8); displays
Ý
suffix with answers
Hex
(hexadecimal number base) Interprets numbers as hexadecimal (base 16); displays
ß
suffix with answers
Non-decimal modes are valid
only on the home screen or i
n
the program editor.
36
Chapter 1: Operating the TI
-
86
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Vector Coordinate Modes
RectV
(rectangular vector coordinates) Displays answers in the form
ã
x y
ä
for two-element
vectors and
ã
x y z
ä
for three-element vectors
CylV
(cylindrical vector coordinates) Displays results in the form
ã
r
±
q
ä
for two-element
vectors and
ã
r
±
q
z
ä
for three-element vectors
SphereV
(spherical vector coordinates) Displays results in the form
ã
r
±
q
ä
for two-element
vectors and
ã
r
±
q
±
f
ä
for three-element vectors
Differentiation Modes
dxDer1
(exact differentiation) Uses
der1
(Chapter 3) to differentiate exactly and calculate the
value for each function in an expression (
dxDer1
is more accurate than
dxNDer
, but it
restricts the kinds of functions that are valid in the expression)
dxNDer
(numeric differentiation) Uses
nDer
to differentiate numerically and calculate the value
for an expression (
dxNDer
is less accurate than
dxDer1
, but more kinds of functions
are valid in the expression)
Vector modes do not affect
how you enter vectors.
The value stored to
d
affects
dxNDer
(Appendix).
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 37 of 10
The CATALOG .................................................................... 38
Storing Data to Variables................................................... 39
Classifying Variables as Data Types...................................42
The CUSTOM Menu ........................................................... 44
The CHAR (Character) Menu.............................................. 45
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
The CATALOG,
Variables, and Characters
2
38
Chapter 2: The
CATALOG
, Variables, and Characters
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 38 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 38 of 10
The CATALOG
-
w
&
The
CATALOG
displays all TI
-
86 functions and instructions in alphabetical order. Items that
do not begin with a letter (such as
+
or
4
Bin
) are at the end of the
CATALOG
.
The selection cursor (
4
) indicates the current item. To select an item from the
CATALOG
,
move the selection cursor to the item and press b. The
CATALOG
disappears and the
name is pasted to the previous cursor location.
Use
#
or
$
to move
4
to
an item...
...and press
b
.
The item is pasted
to the cursor
location.
To jump... Do this:
To the first item beginning with a particular letter Press the letter; ALPHA-lock is on
To special characters at the end of the
CATALOG
Press
$
from the first
CATALOG
item
Down one whole screen Select
PAGE
$
from the
CATALOG
menu (
&
)
Up one whole screen Select
PAGE
#
from the
CATALOG
menu (
'
)
The menu items
CUSTM
and
BLANK
are on the
CATALOG
menu and each
VARS
screen menu.
With them, you can create and edit your own
CUSTOM
menu of up to 15
CATALOG
items and
variables, including program names. For details about the
CUSTOM
menu, read page 44.
The
CATALOG
is the first
item on the
CATLG-VARS
menu.
Chapter 2: The
CATALOG
, Variables, and Characters
39
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 39 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 39 of 10
Storing Data to Variables
On the TI
-
86, data can be stored to variables in several ways. You can:
Use
X
to store a value to a variable.
Use
=
to store an unevaluated expression to an equation variable.
Use an editor’s
Name=
prompt to store several types of data to a variable.
Change TI
-
86 settings or reset defaults and memory to the factory settings.
Execute functions that cause the TI
-
86 to store data automatically to built-in variables.
The TI
-
86 has built-in variable names with specific purposes, such as equation variables, list
names, statistical result variables, window variables, and
Ans
. You can store values to some
of them. They are introduced in the appropriate chapters of this guidebook.
Creating a Variable Name
You can create your own variable name when you use
X
,
=
, or a
Name=
prompt to store
data. When you create a user-created variable name, follow these guidelines.
The user-created variable name can be from one to eight characters long.
The first character must be a letter, which includes all
CHAR
GREEK
menu items, as well
as Ñ, ñ, Ç, and ç from the
CHAR
MISC
menu.
A user-created variable name cannot replicate a TI
-
86 feature symbol or built-in
variable. For example, you cannot create
abs
, because
abs
is the absolute value
function symbol. You cannot create
Ans
, because it is already a built-in variable name.
The TI
-
86 distinguishes between uppercase and lowercase characters in variable
names. For example,
ANS
,
Ans
, and
ans
are three different variable names. Therefore,
only
Ans
is a built-in variable name;
ANS
and
ans
can be user-created variable names.
This chapter describes the
first two data storage
methods listed here. The
other methods are described
in the appropriate chapters.
40
Chapter 2: The
CATALOG
, Variables, and Characters
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 40 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 40 of 10
Storing a Value to a Variable Name
Enter a value, which can be an expression. - ~
5
I
Enter (the store symbol) next to the value. X
Create a variable name one to eight characters
long, starting with a letter. ALPHA-lock is on.
ã
A
ä
ã
R
ä
ã
E
ä
ã
A
ä
Store the value to the variable. The value
stored to the variable is displayed as a result.
b
Storing an Unevaluated Expression
When you store an expression to memory using
X
(with the
sign), the expression is
evaluated and the result is stored to a variable.
When you store an unevaluated expression using
1
ã
=
ä
, or the equation editor
(Chapter 5), or the equation solver (Chapter 15), the unevaluated expression is stored to an
equation variable.
To store an unevaluated expression on the home screen or in a program, the syntax is:
variable
=
expression
where
variable
always precedes the equals sign and
expression
always follows the equals sign.
You can use
=
to store a mathematical expression to an equation variable. For example,
F=M¹A
.
When you use
=
,
variable
is
first, then
=
, then
expression
.
In contrast, when you use
,
value
is first, then
, then
variable
.
Chapter 2: The
CATALOG
, Variables, and Characters
41
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 41 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 41 of 10
Storing an Answer
To store an answer to a variable before you evaluate another expression, use
X
and
Ans
.
Enter and evaluate an expression.
1
1
ã
A
ä
ã
R
ä
ã
E
ä
ã
A
ä
1
M
3
`
3
b
Store the answer to a user-created
variable or to a valid built-in variable.
The value stored to the variable is
displayed as a result.
X
ã
V
ä
ã
O
ä
ã
L
ä
b
Copying a Variable Value
To copy the contents of
variableA
into
variableB
, the syntax is:
variableA
variableB
For example,
RegEqy1
stores the regression equation (Chapter 14) to the variable
y1
.
Displaying a Variable Value
With the cursor on a blank line on the
home screen, paste the variable name to
the cursor location, as described above.
Display the contents of the variable.
-
w
(
#
(location may
vary)
b
b
You also can display variables containing some data types by displaying them in the
appropriate editor (such as the list editor or window variable editor) or graph. These
methods are detailed in subsequent chapters of this guidebook.
In the example, the TI
-
86
multiplies the value stored to
AREA
times
3.3
.
To paste
AREA
to the cursor
location, you can press
-
w
(
, move the
selection cursor
(
4
)
to
AREA
,
and press
b
.
To paste
to the cursor
location, press
X
.
To paste a variable name,
you can select it from a
VARS
menu (page 42).
42
Chapter 2: The
CATALOG
, Variables, and Characters
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 42 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 42 of 10
Recalling a Variable Value
Move the cursor to where you want to
insert the recalled variable value.
100
M
Display the
Rcl
prompt at the bottom of
the screen. ALPHA-lock is on.
Enter the variable name you want to recall.
-
[V] [O] [L]
Recall the variable contents to the cursor
location. The
Rcl
prompt disappears and
the entry cursor returns.
b
Classifying Variables as Data Types
The TI
-
86 classifies variables according to data type and places each variable on a data-type
selection screen. You can display each screen by selecting the appropriate data type from
the
CATLG-VARS
menu, as described on page 43. Here are some examples.
If data... The TI
-
86 classifies the data type as... For example:
Begins with
{
and ends with
}
A list (
VARS LIST
screen)
{1,2,3}
Begins with
ã
and ends with
ä
A vector (
VARS VECTR
screen)
ã
1,2,3
ä
Begins with
ãã
and ends with
ää
A matrix (
VARS MATRX
screen)
ãã
1,2,3
äã
4,5,6
äã
7,8,9
ää
To cancel
RCL
, press
:
.
Editing a recalled value does
not change the value stored
to the variable.
When you store data in an
editor, the TI
-
86 recognizes
the data type according to th
e
editor. For example, only
vectors are stored using the
vector editor.
Chapter 2: The
CATALOG
, Variables, and Characters
43
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 43 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 43 of 10
The CATLG-VARS (CATALOG-Variables) Menu
-
w
CATLG ALL REAL CPLX LIST
4
VECTR MATRX STRNG EQU CONS
4
PRGM GDB PIC STAT WIND
CATLG
Displays the
CATALOG
ALL
Displays a selection screen with all variables and names of all data types
REAL
Displays a selection screen with all real number variables
CPLX
Displays a selection screen with all complex number variables
LIST
Displays a selection screen with all list names
VECTR
Displays a selection screen with all vector names
MATRX
Displays a selection screen with all matrix names
STRNG
Displays a selection screen with all string variables
EQU
Displays a selection screen with all equation variables
CONS
Displays a selection screen with all user-defined constants
PRGM
Displays a selection screen with all program names
GDB
Displays a selection screen with all graph database names
PIC
Displays a selection screen with all picture names
STAT
Displays a selection screen with all statistical result variables
WIND
Displays a selection screen with all window variables
To display additional menu
groups, press
/
.
The list names
fStat
,
xStat
,
and
yStat
are statistical resul
t
variables on the
VARS
STAT
screen.
44
Chapter 2: The
CATALOG
, Variables, and Characters
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 44 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 44 of 10
Selecting a Variable Name
Select the appropriate data-type selection
screen from the
CATLG-VARS
menu.
Move the cursor to the variable you want
to select.
- w (
#
Select the variable you want. b
The CUSTOM Menu
-
w
&
(
You can select up to 15 items from the
CATALOG
and
VARS
screens -- program names, functions,
instructions, and other items -- to create your own
CUSTOM
menu. To display your
CUSTOM
menu, press
9
. Use
&
through
*
and
/
to select items like any other menu.
Entering CUSTOM Menu Items
Select
CUSTM
from the
CATALOG
. The
CUSTOM
menu is displayed. ALPHA-lock is on.
Move the selection cursor (
4
) to the item you
want to copy to the
CUSTOM
menu.
- w
& (
ã
C
ä
# # #
Copy the item to the
CUSTOM
menu cell you
select, replacing any previous item.
To enter more items, repeat steps 2 and 3
using different items and cells.
(
Display the
CUSTOM
menu. -l 9
The example assumes that
the real-number variables
AREA
and
VOL
from the
example on page 41 have no
t
been deleted from memory.
When copying items into the
CUSTOM
menu, you can skip
menu cells and menu groups.
Chapter 2: The
CATALOG
, Variables, and Characters
45
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 45 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 45 of 10
Clearing CUSTOM Menu Items
Select
BLANK
from the
CATALOG
menu. The
CUSTOM BLANK
menu is displayed.
- w
& )
Clear the menu item.
To clear more items, repeat steps 2 and 3.
(
Deleting a Variable from Memory
From the home screen or in a program, to delete from memory one user-created variable
name (except a program name) and its contents, the syntax is:
DelVar(
variable
)
To delete user-created variable names and their contents (including program names), display
the
MEM
DELET
menu (
-
'
), select the data type, select the variable, and then press
b
(Chapter 16). Deleting a variable does not remove it from the
CUSTOM
menu (page 44).
The CHAR (Character) Menu
-
Ÿ
MISC GREEK INTL
miscellaneous international
characters characters menu
menu Greek
characters menu
To clear an item from the
second or third menu group,
press
/
until the item is
displayed, and then select it.
You cannot delete a TI
-
86
built-in variable.
You cannot delete a program
variable using
DelVar(
.
46
Chapter 2: The
CATALOG
, Variables, and Characters
02CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 46 of 1002CATVAR.DOC TI-86, Chap 2, US English Bob Fedorisko Revised: 02/13/01 2:18 PM Printed: 02/13/01 3:00 PM Page 46 of 10
The CHAR MISC (Miscellaneous) Menu
-
Ÿ
&
MISC GREEK INTL
?#&%'
4
!@$~ |
4
¿ÑñÇç
The CHAR GREEK Menu
-
Ÿ
'
MISC GREEK INTL
abg@d4H qlmr
4G s
τ
fJ
The CHAR INTL (International) Menu
-
Ÿ
(
MISC GREEK INTL
´`^¨
You can combine modifiers on the
CHAR
INTL
menu with uppercase or lowercase vowels to
create vowels used in some languages. You can use these vowels in variable names and text.
Adding a Modifier to a Vowel
Select the modifier from the
CHAR
INTL
menu. ALPHA-lock is on. If necessary,
switch to alpha-lock.
Enter the uppercase or lowercase vowel
over which you want the modifier.
-
Ÿ
(
)
-
n
ã
O
ä
Ñ
,
ñ
,
Ç
, and
ç
are valid as
any character of a variable
name, including the first
letter.
%
,
'
, and
!
can be functions.
All
CHAR
GREEK
menu items
are valid variable-name
characters, including the first
letter.
p
(
-
~
)
is not valid
as a character;
p
is a
constant on the TI
-
86.
03MATH.DOC TI-86, Chap 3, US English Bob Fedorisko Revised: 02/13/01 2:19 PM Printed: 02/13/01 3:00 PM Page 47 of 10
Keyboard Mathematical Functions .................................... 48
The MATH Menu................................................................ 49
The CALC (Calculus) Menu ................................................54
The TEST (Relational) Menu............................................... 55
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Math, Calculus,
and Test Operations
3
48
Chapter 3: Math, Calculus, and Test Operations
03MATH.DOC TI-86, Chap 3, US English Bob Fedorisko Revised: 02/13/01 2:19 PM Printed: 02/13/01 3:00 PM Page 48 of 1003MATH.DOC TI-86, Chap 3, US English Bob Fedorisko Revised: 02/13/01 2:19 PM Printed: 02/13/01 3:00 PM Page 48 of 1003MATH.DOC TI-86, Chap 3, US English Bob Fedorisko Revised: 02/13/01 2:19 PM Printed: 02/13/01 3:00 PM Page 48 of 10
Keyboard Mathematical Functions
You can use these mathematical functions in expressions with real or complex values. You
can use some of them with lists, vectors, matrices, or strings.
When you use lists, vectors, or matrices, the valid functions return a list of results calculated
on an element-by-element basis. If you use two lists, vectors, or matrices in the same
expression, they must be equal in dimension.
Key Function Key Function
\
+
(add)
=
sin
(sine)
T
N
(subtract)
>
cos
(cosine)
M
¹
(multiply)
?
tan
(tangent)
F
à
(divide)
-
{
sin
L
1
(arcsine; inverse of sine)
a
M
(negate)
-
|
cos
L
1
(arccosine; inverse of cosine)
I
2
(square)
-
}
tan
L
1
(arctangent; inverse of tangent)
-
ˆ
(square root)
<
log
(logarithm)
-
ƒ
L
1
(inverse)
B
ln
(natural log)
@
^
(raise to a specified power)
-
e
x
(constant
e
raised to a power)
-
z
10^
(10 to a specified power)
-
~
p
(constant pi; 3.1415926535898)
C
E
(exponent)
The A to Z Reference details
which data types are valid
arguments for each function.
The most common
mathematical functions are
on the TI
-
86 keyboard. For
syntax, details, and example
s
of these functions, refer to
the A to Z Reference.
x
-
1
(the multiplicative inverse
)
is equivalent to the
reciprocal, 1
à
x.
Chapter 3: Math, Calculus, and Test Operations
49
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The MATH Menu
-
Œ
NUM PROB ANGLE HYP MISC
4
INTER
number angle miscellaneous math
menu menu functions menu
probability hyperbolic interpolate
menu menu editor
The MATH NUM (Number) Menu
-
Œ
&
NUM PROB ANGLE HYP MISC
round iPart fPart int abs
4
sign min max mod
round(
value
[
,
#ofDecimals
]
)
Rounds
value
to 12 decimal places or to
#ofDecimals
iPart
value
Returns the integer part or parts of
value
fPart
value
Returns the fractional part or parts of
value
int
value
Returns the largest integer less than or equal to
value
abs
value
Returns the absolute value or magnitude of
value
sign
value
Returns
1
if
value
is positive;
0
if
value
is
0
;
L
1
if
value
is negative
min(
valueA
,
valueB
)
Returns the smaller of
valueA
and
valueB
min(
list
)
Returns the smallest element of
list
max(
valueA
,
valueB
)
Returns the larger of
valueA
and
valueB
max(
list
)
Returns the largest element of
list
mod(
numberA
,
numberB
)
Returns
numberA
modulo
numberB
value
can sometimes be an
expression, list, vector, or
matrix. For details about
specific syntax options and
examples, refer to the A to Z
Reference.
50
Chapter 3: Math, Calculus, and Test Operations
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The MATH PROB (Probability) Menu
-
Œ
'
NUM PROB ANGLE HYP MISC
! nPr nCr rand randIn
4
randN randBi
value
!
Returns the factorial of a real
value
items
nPr
number
Returns the number of permutations of
items
(
n
) taken
number
(
r
) at a
time
items
nCr
number
Returns the number of combinations of
items
(
n
) taken
number
(
r
) at a
time
rand
Returns a random number > 0 and < 1; to control a random number
sequence, first store an integer seed value to
rand
(such as
0
rand
)
randInt(
lower
,
upper
ã
,
#ofTrialsä
)
(random integer) Returns a random integer bound by the specified
integers,
lower
integer
upper
; to return a list of random integers,
specify an integer > 1 for
#ofTrials
randNorm(
mean
,
stdDeviation
ã
,
#ofTrialsä
)
(random normal) Returns a random real number from a normal
distribution specified by
mean
and
stdDeviation
; to return a list of
random numbers, specify an integer > 1 for
#ofTrials
randBin(
#ofTrials
,
probabilityOfSuccess
ã
,
#ofSimulationsä
)
(random binomial) Returns a random real number from a binomial
distribution, where
#ofTrials
1 and 0
probabilityOfSuccess
1; to
return a list of random numbers, specify an integer > 1 for
#ofSimulations
!
(factorial) is valid for non-
integers.
randInt
,
randNorm
, and
randBin
are abbreviated in
the
MATH
PROB
menu.
Chapter 3: Math, Calculus, and Test Operations
51
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The MATH ANGLE Menu
-
Œ
(
NUM PROB ANGLE HYP MISC
or '
4
DMS
angle
¡
Overrides current angle mode setting to express
angle
in degrees
angle
r
Overrides current angle mode setting to express
angle
in radians
degrees
'
minutes
'
seconds
'
Designates an angle as
degrees
,
minutes
, and
seconds
angle
4
DMS
Displays
angle
in degrees
¡
minutes'seconds" format, even though you use
degrees
'
minutes
'
seconds
'
to enter a DMS angle
The MATH HYP (Hyperbolic) Menu
-
Œ
)
NUM PROB ANGLE HYP MISC
sinh cosh tanh sinh
-
1
cosh
-
1
4
tanh
-
1
sinh
value
Returns the hyperbolic sine of
value
cosh
value
Returns the hyperbolic cosine of
value
tanh
value
Returns the hyperbolic tangent of
value
sinh
L
1
value
Returns the hyperbolic arcsine of
value
cosh
L
1
value
Returns the hyperbolic arccosine of
value
tanh
L
1
value
Returns the hyperbolic arctangent of
value
angle
can be a list for
¡
,
r
,
and
4
DMS
.
In a calculation, the result of
a
degrees
'
minutes
'
seconds
'
entry is treated as degrees in
Degree
angle mode only. It is
treated as radians in
Radian
angle mode.
value
can sometimes be an
expression, list, vector, or
matrix. For details about
specific syntax options and
examples, refer to the A to Z
Reference.
52
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The MATH MISC (Miscellaneous) Menu
-
Œ
*
NUM PROB ANGLE HYP MISC
sum prod seq lcm gcd
44
Frac % pEval
x
eval
sum
list
Returns the sum of the elements of
list
prod
list
Returns the product of the elements of
list
seq(
expression
,
variable
,
begin
,
end
[
,
step
]
)
Returns a list in which each element is the value of
expression
evaluated for
variable
from
begin
to
end
by
step
lcm(
valueA
,
valueB
)
Returns the least common multiple of
valueA
and
valueB
gcd(
valueA
,
valueB
)
Returns the greatest common divisor of
valueA
and
valueB
value
4
Frac
Displays
value
as a fraction
value
%
Returns
value
divided by 100 (multiplied by .01)
p
ercent
%
number
Returns
percent
of
number
pEval(
coefficientList
,
xValue
)
Returns the value of a polynomial (whose coefficients are given in
coefficientList
) at
xValue
x
th
root
x
value
Returns the
x
th
root
of
value
eval
value
Returns a list of the values of all selected functions in the current
graphing mode for the real
value
of the independent variable
value
can sometimes be an
expression, list, vector, or
matrix. For details about
specific syntax options, refer
to the A to Z Reference.
Chapter 3: Math, Calculus, and Test Operations
53
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The Interpolate
à
Extrapolate Editor
-
Œ
/
&
Using the interpolate
à
extrapolate editor, you can interpolate or extrapolate a value linearly,
given two known pairs and the x-value or y-value of the unknown pair.
Display the interpolate
à
extrapolate editor.
Enter real values for the first known pair
(
x1
,
y1
). The values can be expressions.
-
Œ
/
&
3
b
5
b
Enter values for the second known pair
(
x2
,
y2
).
4
b
4
b
Enter a value for either the
x
value or the
y
value of the unknown pair.
If necessary, move the cursor to the value
for which you want to solve (
x
or
y
).
Select
SOLVE
.
1
b
$
or
#
*
The result is interpolated or extrapolated and displayed; the variables
x
and
y
are not
changed. A solid square in the first column indicates the interpolated or extrapolated value.
After solving for a value, you can continue to use the interpolate
à
extrapolate editor.
To interpolate y from the
home screen, select
inter(
from the
CATALOG
, and then
enter
inter(
x1
,
y1
,
x2
,
y2
,
x
)
.
To interpolate x from the
home screen, enter
inter(
y1
,
x1
,
y2
,
x2
,
y
)
.
You can store individual
values with the
X
key
(Chapter 2).
54
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The CALC (Calculus) Menu
-
evalF nDer der1 der2 fnInt
4
fMin fMax arc
The calculus functions return values with respect to any user-created variable, to built-in
variables
eqn
and
exp
, and to graphing variables such as
x
,
t
, and
q
.
evalF(
expression
,
variable
,
value
)
Returns the value of
expression
with respect to
variable
for a
given variable
value
nDer(
expression
,
variable ã
,
valueä
)
Returns an approximate numerical derivative of
expression
with
respect to
variable
for the current variable value or specified
v
ariable
value
der1(
expression
,
variableã
,
valueä
)
Returns the value of the first derivative of
expression
with respect to
variable
for the current variable value or specified variable
value
der2(
expression
,
variableã
,
valueä
)
Returns the value of the second derivative of
expression
with respect
to
variable
for the current variable value or specified variable
value
fnInt(
expression
,
variable
,
lower
,
upper
)
Returns the numerical integral of
expression
with respect to
variable
between
lower
and
upper
boundaries
fMin(
expression
,
variable
,
lower
,
upper
)
Returns the minimum value of
expression
with respect to
variable
between
lower
and
upper
boundaries
fMax(
expression
,
variable
,
lower
,
upper
)
Returns the maximum value of
expression
with respect to
variable
between
lower
and
upper
boundaries
arc(
expression
,
variable
,
start
,
end
)
Returns the length of a segment of a curve defined by
expression
with respect to
variable
between
start
and
end
You must set
Dec
mode to
use the calculus functions.
For
evalF
,
nDer
,
der1
, and
der2
,
variable
can be a real
or complex number or list.
You can use
der1
and
der2
in
expression
. You can use
nDer
once in
expression
.
For
fnInt
,
fMin
, and
fMax
,
lower
<
upper
must be true.
Chapter 3: Math, Calculus, and Test Operations
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The built-in variable
d
defines the step size in calculating
nDer(
(in
dxNDer
differentiation
mode only) and
arc(
. The built-in variable
tol
defines the tolerance in calculating
fnInt(
,
fMin(
,
fMax(
, and
arc(
. The value of each must be >0. These factors affect the accuracy of the
calculations. As
d
becomes smaller, the approximation typically is more accurate. For
example,
nDer(A^3,A,5)
returns
75.0001
if
d
=.01
, but returns
75
if
d
=.0001
(Appendix).
The function integral error value is stored to the variable
fnIntErr
(Appendix).
For
arc(
and
fnInt(
while
dxDer1
mode is set, these functions are not valid in
expression
:
evalF(
,
der1(
,
der2(
,
fMin(
,
fMax(
,
nDer(
,
seq(
, and any equation variable, such as
y1
.
You can approximate the fourth derivative at the current value of x with this formula:
nDer(nDer(der2(x^4,x),x),x)
.
The TEST (Relational) Menu
-
˜
= = < >
‚4ƒ
valueA
==
valueB
(equal to) Returns
1
if
valueA
is equal to
valueB
; returns
0
if not equal;
valueA
and
valueB
can be real or complex numbers, lists, vectors, matrices, or strings
valueA
<
valueB
(less than) Returns
1
if
valueA
is less than
valueB
; returns
0
if
valueA
is not less than
valueB
;
valueA
and
valueB
must be real numbers or lists
valueA
>
valueB
(greater than) Returns
1
if
valueA
is greater than
valueB
; returns
0
if
valueA
is not
greater than
valueB
;
valueA
and
valueB
must be real numbers or lists
valueA
valueB
(less than or equal to) Returns
1
if
valueA
is less than or equal to
valueB
; returns
0
if
valueA
is not less than or equal to
valueB
;
valueA
and
valueB
must be real numbers or lists
Relational functions are valid
for two lists of the same
length. When
valueA
and
valueB
are lists, a list of
results calculated element by
element is returned.
56
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valueA
valueB
(greater than or equal to) Returns
1
if
valueA
is greater than or equal to
valueB
;
returns
0
if
valueA
is not greater than or equal to
valueB
;
valueA
and
valueB
must be
real numbers or lists
valueA
ƒ
valueB
(not equal to) Returns
1
if
valueA
is not equal to
valueB
; returns
0
if
valueA
is equal
to
valueB
;
valueA
and
valueB
can be real or complex numbers, lists, vectors,
matrices, or strings
Using Tests in Expressions and Instructions
The TI
-
86 Evaluation Operating System (Appendix) performs all operations except Boolean
operators before it performs relational functions. For example:
The expression
2+2==2+3
evaluates to
0
. The TI
-
86 performs the addition first, and then
compares 4 to 5.
The expression
2+(2==2)+3
evaluates to
6
. The TI
-
86 performs the test in parentheses
first, and then adds 2, 1, and 3.
You can use relational
functions to control program
flow (Chapter 16).
04CCCB.DOC TI-86, Chap 4, US English Bob Fedorisko Revised: 02/13/01 2:20 PM Printed: 02/13/01 3:01 PM Page 57 of 16
Using Built-In and User-Created Constants .......................58
Converting Units of Measure.............................................61
Number Bases.................................................................... 65
Using Complex Numbers ...................................................70
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
4
Constants, Conversions,
Bases, and Complex Numbers
58
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Using Built-In and User-Created Constants
A constant is a variable with a specific value stored to it. The
CONS
BLTIN
menu items are
common constants built into the TI
-
86. You cannot edit the value of a built-in constant.
You can create your own constants and add them to the user-created constant menu for
easy access. To enter a user-created constant, you must use the user-created constant
editor (page 60); you cannot use
X
or
=
to create a constant.
The CONS (Constants) Menu
-
BLTIN EDIT USER
built-in user-created
constants menu constants menu
user-created
constants editor
The CONS BLTIN (Built-In Constants) Menu
-
&
BLTIN EDIT USER
Na k Cc ec Rc
4
Gc g Me Mp Mn
4m
0
H
0h c u
You can select built-in
constants from the
CONS BLTIN
menu or enter
them using the keyboard and
the
CHAR GREEK
menu.
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
59
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Built-In Constant Constant Name Constant Value
Na
Avogadro's number 6.0221367
E
23 mole
L
1
k
Boltzman's constant 1.380658
E
L
23 J
à
K
Cc
Coulomb constant 8.9875517873682
E
9 N m
2
à
C
2
ec
Electron charge 1.60217733
E
L
19 C
Rc
Gas constant 8.31451 J
à
mole K
Gc
Gravitational constant 6.67259
E
L
11 N m
2
à
kg
2
g
Earth acceleration due to gravity 9.80665 m
à
sec
2
Me
Mass of an electron 9.1093897
E
L
31 kg
Mp
Mass of a proton 1.6726231
E
L
27 kg
Mn
Mass of a neutron 1.6749286
E
L
27 kg
m
0
Permeability of a vacuum 1.2566370614359
E
L
6 N
à
A
2
H
0
Permittivity of a vacuum 8.8541878176204
E
L
12 F
à
m
h
Planck's constant 6.6260755
E
L
34 J sec
c
Speed of light in a vacuum 299,792,458 m
à
sec
u
Atomic mass unit 1.6605402
E
L
27 kg
p
Pi 3.1415926535898
e
Base of natural log 2.718281828459
To use
p
, press
-
~
or
select it from the
CATALOG
.
To use
e^
, press
-
.
To use
e
, press
-
n
ã
E
ä
.
60
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Creating or Redefining a User-Created Constant
Display the
CONS
menu. -
Display the constant editor. The
Name=
prompt,
Value=
prompt, and
CONS
USER
menu are displayed. ALPHA-lock is on.
'
Enter a constant name. Either enter a new name
one to eight characters long, starting with a letter,
or select a name from the
CONS
USER
menu.
The cursor moves to the
Value=
prompt and the
CONS
EDIT
menu is displayed (see below).
ã
A
ä
- n
ã
U
ä
b
Enter the real or complex constant value, which
can be an expression. The value is stored to the
constant as you enter it. The user-created
constant becomes a
CONS
USER
menu item.
196
`
9665
The Constant Editor Menu
-
'
name
b
or
#
PREV NEXT DELET
PREV
Displays the name and value (if any) of the previous constant on the
CONS
USER
menu
NEXT
Displays the name and value (if any) of the next constant on the
CONS
USER
menu
DELET
Deletes the name and value of the constant currently displayed in the constant editor
CONS
USER
menu items are
the names of all stored user-
created constants, arranged
alphanumerically.
196.9665 is the atomic
weight of gold (Au).
You can enter a value later.
If you select
PREV
when the
first constant name is
displayed, or
NEXT
when the
last constant name is
displayed, the
CONS
USER
menu replaces the
CONS
EDIT
menu.
You also can delete a
constant from the
MEM
DELET
CONS
screen.
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
61
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Entering a Constant Name in an Expression
You can enter a constant in an expression in any of three ways.
Select the constant name from the
CONS
BLTIN
menu or the
CONS
USER
menu.
Select a user-created constant name from the
VARS CONS
screen.
Use the ALPHA keys, alpha keys, and other character keys to enter a constant name.
Converting Units of Measure
With the TI
-
86, you can convert a value measured in one unit into its equivalent value in
another unit of measure. For example, you can convert inches to yards, quarts to liters, or
degrees Fahrenheit to degrees Celsius.
The units of measure from which and to which you convert must be compatible. For
example, you cannot convert inches to degrees Fahrenheit, or yards to calories. Each menu
item on the
CONV
menu (page 62) represents a unit-of-measure group, such as length
(
LNGTH
), volume (
VOL
), and pressure (
PRESS
). Within each menu, all units are compatible.
Converting a Unit of Measure
To use any conversion instruction, the syntax is:
(
value
)
currentUnit
4
newUnit
Enter the real
value
to be converted.
Display the
CONV
menu.
Select the
TEMP
conversion group.
D
a
2
E
-
*
You can enter a conversion
expression anywhere that an
expression is valid.
In the example,
L
2
degrees
Celsius is converted to
degrees Fahrenheit.
Always use parentheses
when
value
is negative.
62
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Select the current unit of measure (
¡
C
) from the
conversion group menu. The unit abbreviation
and conversion symbol (
4
) are pasted to the
cursor location.
&
Select the new unit of measure (
¡
F
) from the
conversion group menu. The unit abbreviation is
pasted to the cursor location.
Convert the measurement.
'
b
The CONV (Conversions) Menu
-
LNGTH AREA VOL TIME TEMP
4
MASS FORCE PRESS ENRGY POWER
4
SPEED
length volume temperature speed force energy
menu menu menu menu menu menu
area menu time menu mass menu pressure menu power menu
Important:
When you convert a negative value, you must enclose in parentheses the value
and its negation sign, as in
(
L
4)
. Otherwise, the TI
-
86 order of evaluation will perform the
conversion first, and then apply the negation to the converted value.
If you enter... ...The TI
-
86 converts it to...
(
L
4)
¡
C
F
24.8
degrees Fahrenheit (
L
4
¡
Celsius converted to degrees Fahrenheit)
L
4
¡
C
F
L
39.2
degrees Fahrenheit (4
¡
Celsius converted to degrees Fahrenheit, then negated)
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
63
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The CONV LNGTH (Length) Menu
-
&
mm
millimeters
yd
yards
mil
mils
cm
centimeters
km
kilometers
Ang
Angstroms
m
meters
mile
miles
fermi
fermis
in
inches
nmile
nautical miles
rod
rods
ft
feet
lt-yr
light-years
fath
fathoms
The CONV AREA Menu
-
'
ft
2
square feet
km
2
square kilometers
cm
2
square centimeters
m
2
square meters
acre
acres
yd
2
square yards
mi
2
square miles
in
2
square inches
ha
hectares
The CONV VOL (Volume) Menu
-
(
liter
liters
cm
3
cubic centimeters
tsp
teaspoons
gal
gallons
in
3
cubic inches
tbsp
tablespoons
qt
quarts
ft
3
cubic feet
ml
milliliters
pt
pints
m
3
cubic meters
galUK
UK gallons
oz
ounces
cup
cups
ozUk
UK ounces
The CONV TIME Menu
-
)
sec
seconds
day
days
ms
milliseconds
mn
minutes
yr
years
m
s
microseconds
hr
hours
week
weeks
ns
nanoseconds
The CONV TEMP (Temperature) Menu
-
*
¡
C
degrees Celsius
¡
F
degrees Fahrenheit
¡
K
degrees Kelvin
¡
R
degrees Rankin
64
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
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The CONV MASS Menu
-
/
&
gm
grams
amu
atomic mass units
ton
tons
kg
kilograms
slug
slugs
mton
metric tons
lb
pounds
The CONV FORCE Menu
-
/
'
N
Newtons
tonf
ton force
lbf
pound force
dyne
dynes
kgf
kilogram force
The CONV PRESS (Pressure) Menu
-
/
(
atm
atmospheres
lb
à
in
2
pounds per square inch
inHg
inches of mercury
bar
bars
mmHg
millimeters of mercury
inH
2
O
inches of water
N
à
m
2
Newtons per square meter
mmH
2
millimeters of water
The CONV ENRGY (Energy) Menu
-
/
)
J
oules
ft-lb
foot-pounds
erg
ergs
cal
calories
kw-hr
kilowatt hours
l-atm
liter-atmospheres
Btu
British thermal units
eV
electron Volts
The CONV POWER Menu
-
/
*
hp
horsepower
ftlb
à
s
foot-pounds per second
Btu
à
m
British thermal units
W
Watts
cal
à
s
calories per second per minute
The CONV SPEED Menu
-
/
/
&
ft
à
s
feet per second
mi
à
hr
miles per hour
knot
knots
m
à
s
meters per second
km
à
hr
kilometers per hour
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
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Converting a Value Expressed as a Rate
To convert a value expressed as a rate on the home screen, you can use parentheses and
the division operator (
à
). For example, if a car travels 325 miles in 4 hours, and you want
to know the rate of speed in kilometers per hour, enter this expression:
(325
à
4)mi
à
hr
4
km
à
hr
This expression returns
131
km
à
hr (rounded up).
You also can return this result using only a forward slash, as in:
325mile
4
km
à
4hr
4
hr
Number Bases
The number base mode setting (Chapter 1) controls how the TI
-
86 interprets an entered
number and displays results on the home screen. However, you can enter numbers in any
number base using number base designators
Ü
,
Ý
,
Þ
, and
ß
. Then you can display the result
on the home screen in any number base using number base conversions.
All numbers are stored internally as decimal. If you perform an operation in a mode setting
other than
Dec
, the TI
-
86 performs integer mathematics, truncating to an integer after every
calculation and expression.
For example, in
Hex
mode,
1
à
3+7
returns
7h
(1 divided by 3, truncated to 0, and then added to 7).
To enter a forward slash
(
à
)
, you can use the
F
key
or paste it from the
CATALOG
.
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Number Base Ranges
Binary, octal, and hexadecimal numbers on the TI
-
86 are defined in these ranges.
Type Low Value
à
High Value Decimal Equivalent
Binary 1000 0000 0000 0001
b
0111 1111 1111 1111
b
L
32,767
32,767
Octal 5120 6357 4134 0001
o
2657 1420 3643 7777
o
L
99,999,999,999,999
99,999,999,999,999
Hexadecimal
ÚÚÚÚ
Õ
50
×
ÙÚ
85
×
001
h
0000 5
ÕÚ
3 107
Õ
3
ÚÚÚ
h
L
99,999,999,999,999
99,999,999,999,999
One’s and Two’s Complements
To obtain the one's complement of a binary number, enter the
not
function (page 68) before
the number. For example,
not
111100001111
in
Bin
mode returns
1111000011110000
Ü
.
To obtain the two's complement of a binary number, press
a
before entering the number.
For example,
L
111100001111
in
Bin
mode returns
1111000011110001
Ü
.
The (Number) BASE Menu
-
Õ
-
Ú
TYPE CONV BOOL BIT
hexadecimal base conversion rotate
à
shift
characters menu menu
menu base type Boolean operator
menu menu
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
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The BASE
Õ
-
Ú
(Hexadecimal Characters) Menu
-
&
This is the
BASE
Õ
-
Ú
menu displayed on the home screen. To use
Õ
, press
-
e
.
Õ
TYPE CONV BOOL BIT
Ö×ØÙÚ
When an editor menu is the upper menu,
Õ
and ...
Õ
and
Ö
move to two separate cells, and
Ù
and
Ú
Ö
are combined in one cell. If you press
&
or
/
... are combined. To switch back, press
*
or
/
.
{ } NAMES " OPS { } NAMES " OPS
Õ
-
Ö× Ø Ù Ú
4
ÕÖ×ØÙ
-
Ú
Entering Hexadecimal Digits
To enter a hexadecimal number, use the number keys as you would for a decimal number.
Select the hexadecimal characters
Õ
through
Ú
from the menu as needed.
The BASE TYPE Menu
-
'
Õ
-
Ú
TYPE
CONV BOOL BIT
ÜßÝÞ
In an expression, you can designate a number in any number base, regardless of mode.
After you enter the number, select the appropriate base type symbol from the
BASE TYPE
menu. The base type symbol is pasted to the cursor location. Here are some examples.
In
Dec
mode (default):
10
Ü
+10
b
12
10
ß
+10
b
26
In
Oct
mode:
10
Ü
+10
b
12
Ý
10
Þ
+10
b
22
Ý
In
Bin
mode:
10
ß
+10
b
10010
Ü
10
Þ
+10
b
1100
Ü
In
Hex
mode:
10
Ü
+10
b
12
ß
10
Þ
+10
b
1
Õß
BASE
Õ
-
Ú
menu items and
BASE TYPE
menu items are
not the same as regular
alphabetical characters.
In the example, the upper
menu is the list editor menu
(
-
in
Dec
number
base mode).
If
Hex
number base mode is
not set, you must enter the
ß
designator, even if the
number contains a special
hexadecimal character.
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The BASE CONV (Conversion) Menu
-
(
Õ
-
Ú
TYPE CONV BOOL BIT
4
Bin
4
Hex
4
Oct
4
Dec
value
4
Bin
Displays
value
as binary
value
4
Oct
Displays
value
as octal
value
4
Hex
Displays
value
as hexadecimal
value
4
Dec
Displays
value
as decimal
Converting Number Bases
In
Dec
mode, solve
10
Ü
+
Úß
+ 10
Ý
+ 10
.
10
Ü
+
Úß
+10
Ý
+10
b
35
Add
1
to the result and convert it to
Bin
number base display.
Ans+1
4
Bin
b
100100
Ü
Add
1
to the result and convert it to
Hex
number base display.
Ans+1
4
Hex
b
25
ß
Add
1
to the result and convert it to
Oct
number base display.
Ans+1
4
Oct
b
46
Ý
Add
1
to the result and convert it to
Dec
number base display.
Ans+1
b
39
The BASE BOOL (Boolean) Menu
-
)
Õ
-
Ú
TYPE CONV BOOL BIT
and or xor not
valueA
and
valueB valueA
or
valueB valueA
xor
valueB
not
value
value
can be an expression,
list, vector, or matrix. For
detailed syntax descriptions,
refer to the A to Z Reference.
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
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Results of Boolean Operations
When a Boolean expression is evaluated, the arguments are converted to hexadecimal
integers and the corresponding bits of the arguments are compared, as this table shows.
Results
If
valueA
is... ...and
valueB
is...
and or xor not
(
valueA
)
1 1 1100
1 0 0110
0 1 0111
0 0 0001
The result is displayed according to the current mode setting. For example:
In
Bin
mode,
101 and 110
returns
100Ü
.
In
Hex
mode,
5 and 6
returns
4ß
.
The BASE BIT Menu
-
*
Õ
-
Ú
TYPE CONV BOOL BIT
rotR rotL shftR shftL
rotR
value
Rotates
value
right
rotL
value
Rotates
value
left
shftR
value
Shifts
value
right
shftL
value
Shifts
value
left
Both the argument and the
result must be within defined
number ranges (page 66).
Rotate and shift operate on
16 base digits. To minimize
an overflow error, enter the
argument in binary form.
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Using Complex Numbers
A complex number has two components: real (a) and imaginary (+b
i
). On the TI
-
86, you
enter the complex number a+b
i
as:
(
real
,
imaginary
)
in rectangular form
(
magnitude
±
angle
)
in polar form
You can enter a complex number in rectangular or polar form, regardless of the current
complex number mode setting. The separator (
,
or
±
) determines the form.
To enter rectangular form, separate
real
and
imaginary
with a comma (
P
).
To enter polar form, separate
magnitude
and
angle
with an angle symbol (
-
).
Each component (
real
,
imaginary
,
magnitude
, or
angle
) can be a real number or an
expression that evaluates to a real number; expressions are evaluated when you press
b
.
When
RectC
complex number mode is set, complex
numbers are displayed in rectangular form, regardless of
the form in which you enter them (as shown to the right).
When
PolarC
complex number mode is set, complex
numbers are displayed in polar form, regardless of the
form in which you enter them (as shown to the right).
Complex Results
Complex numbers in results, including list, matrix, and vector elements, are displayed in
the form (rectangular or polar) specified by the mode setting (Chapter 1) or by a display
conversion instruction (page 61).
When
Radian
angle mode is set, results are displayed as
(
magnitude
±
angle
)
.
When
Degree
angle mode is set, results are displayed as
(
real
,
imaginary
)
.
Variable names with complex
numbers stored to them are
listed on the
VARS CPLX
screen (Chapter 2).
Lists, matrices, and vectors
can have complex elements.
The graph format settings
RectGC
and
PolarGC
(Chapter 5) determine the
complex number form of
graph screen coordinates.
Chapter 4: Constants, Conversions, Bases, and Complex Numbers
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For example, when
PolarC
and
Degree
modes are set,
(2,1)
N
(1
±
45)
returns
(1.32565429614
±
12.7643896828)
.
Using a Complex Number in an Expression
Enter the complex number directly.
Use the ALPHA keys, alpha keys, and other character keys to enter a complex variable.
Select a complex variable from the
VARS CPLX
screen.
The CPLX (Complex Number) Menu
-
conj real imag abs angle
4 4
Rec
4
Pol
conj (real,imaginary)
Returns the complex conjugate of a complex value, list, vector or
matrix; the result is
(real,
L
imaginary)
conj (magnitude
±
angle)
Returns
(magnitude
±L
angle)
real (real,imaginary)
Returns the real portion of a complex number, list, vector, or matrix as
a real number; the result is
real
real (magnitude
±
angle)
Returns
magnitude
¹
cosine(
angle
)
imag (real,imaginary)
Returns the imaginary (non-real) portion of a complex number, list,
v
ector, or matrix as a real number; the result is
imaginary
imag (magnitude
±
angle)
Returns
magnitude
¹
sine(
angle
)
abs (real,imaginary)
(Absolute value) Returns the magnitude (modulus) of a complex
number, list, vector, or matrix of complex numbers; the result is
(
real
2
+
imaginary
2
)
abs (magnitude
±
angle)
Returns
magnitude
You can enter the name or a
complex list, vector, or matrix
as an argument for any
CPLX
menu item.
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angle (real,imaginary)
Returns the polar angle of a complex number, list, vector, or matrix
calculated as
tan
L
1
(imaginary
à
real)
(adjusted by
p
in the second
quadrant or
L
p
in the third quadrant); the result is tan
L
1
(
imaginaryàreal
)
angle (magnitude
±
angle)
Returns
angle
(where
L
p
<
anglep
)
complexValue
4
Rec
Displays
complexValue
in rectangular format
(real,imaginary)
,
regardless of complex mode setting; valid only at the end of a command
and only when
complexValue
is indeed complex
complexValue
4
Pol
Displays
complexValue
in polar format (
magnitude
±
angle
), regardless
of complex mode setting; valid only at the end of a command and only
when
complexValue
is indeed complex
You can enter a complex list, vector, or matrix directly. The syntax below is for lists. To
enter a complex vector or matrix, substitute brackets for braces below and use the correct
form for either data type (Chapters 12 and 13).
In rectangular form, to use lists of complex numbers with
conj
,
real
,
imag
,
abs
, and
angle
, the
syntax is:
conj{(
realA
,
imaginaryA
),(
realB
,
imaginaryB
),(
realC
,
imaginaryC
),
...
}
In polar form, to use lists of complex numbers with
conj
,
real
,
imag
,
abs
, and
angle
, the
syntax is:
real{(
magnitudeA
±
angleA
),(
magnitudeB
±
angleB
),(
magnitudeC
±
angleC
),
...
}
When you use a list the TI
-
86 calculates the result element by element and returns a list, in
which each element is expressed according to the complex mode setting.
Select
{
and
}
from the
LIST
menu.
You must enter commas to
separate list elements.
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Defining a Graph................................................................ 74
Setting the Graph Mode .................................................... 74
The GRAPH Menu .............................................................. 75
Using the Equation Editor..................................................76
Setting the Window Variables ...........................................81
Setting the Graph Format ..................................................83
Displaying a Graph ............................................................85
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Function Graphing
5
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Defining a Graph
This chapter describes the process for graphing functions in
Func
graphing mode, but the
process is similar for each TI
-
86 graphing mode. Chapters 8, 9, and 10 describe the unique
aspects of polar, parametric, and differential equation graphing modes. Chapter 6 describes
various graphing tools, many of which you can use in all graphing modes.
Set the graphing mode (page 74).
Define, edit, or select one or more functions in the equation editor (pages 76 and 77).
Select the graph style for each function (page 79).
Deselect stat plots, if necessary (page 81).
Set the viewing window variables (page 81).
Select the graph format settings (page 83).
Setting the Graph Mode
To display the mode screen, press
-
m
. All default mode
settings, including
Func
graphing mode, are highlighted in the
p
icture to the right. The graphing modes are on the fifth line.
Func
(function graphing)
Pol
(polar graphing; Chapter 8)
Param
(parametric graphing; Chapter 9)
DifEq
(differential equation graphing; Chapter 10)
Some of these steps are not
necessary every time you
define a graph.
Chapter 5: Function Graphing
75
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Each graphing mode has a unique equation editor. You must select the graphing mode and
Dec
number base mode before you enter the functions. The TI
-
86 retains in memory all
equations stored to the
Func
,
Pol
,
Param
, and
DifEq
equation editors. Each mode also has
unique graph format settings and window variables.
Stat plot on
à
off status, zoom factors, mode settings, and tolerance apply to all graphing
modes; changing the graphing mode does not affect them.
These mode settings affect graphing results.
Radian
or
Degree
angle mode affects the interpretation of some functions.
dxDer1
or
dxNDer
differentiation mode affects plotting of selected functions.
The GRAPH Menu
6
y(x)= WIND ZOOM TRACE GRAPH
4
MATH DRAW FORMT STGDB RCGDB
4
EVAL STPIC RCPIC
y(x)=
Displays the equation editor; use this screen to enter functions to be graphed
WIND
Displays the window editor; use this editor to change graph screen dimensions
ZOOM
Displays the
GRAPH
ZOOM
menu; use these items to change the graph screen dimensions
TRACE
Activates the trace cursor; use this cursor to trace along the graph of a specific function
GRAPH
Displays the graph screen; graphs all selected functions and turned on stat plots
MATH
Displays the
GRAPH
MATH
menu; use this menu to explore graphs mathematically
DRAW
Displays the
GRAPH
DRAW
menu; use this menu to draw on graphs or test pixels
Chapter 1 describes all mode
settings in detail.
Chapter 6 describes these
GRAPH
menu items:
ZOOM
,
TRACE
,
MATH
,
DRAW
,
STGDB
,
RCGDB
,
EVAL
,
STPIC
, and
RCPIC
.
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Chapter 5: Function Graphing
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FORMT
Displays the graph format screen; use this screen to select graph format settings
STGDB
Displays the
Name=
prompt and
STGDB
menu; use this prompt to enter a
GDB
variable
RCGDB
Displays the
Name=
prompt and
RCGDB
menu; use this menu to recall a graph database
EVAL
Displays the
Eval x=
prompt; enter an
x
for which you want to solve the current function
STPIC
Displays the
Name=
prompt and
STPIC
menu; use this prompt to enter a
PIC
variable
RCPIC
Displays the
Name=
prompt and
RCPIC
menu; use this menu to recall a picture
Using the Equation Editor
To display the equation editor in
Func
graphing mode, select
y(x)=
from the
GRAPH
menu (
6
&
). The
GRAPH
menu
shifts up and the equation editor menu is displayed as the
lower menu. You can store up to 99 functions in the
equation editor, if sufficient memory is available.
If a function is selected, its equals sign (=) is highlighted in the equation editor. If the
function is deselected, its equals sign is not highlighted. Only selected functions are plotted
when the TI
-
86 plots a graph.
The Equation Editor (GRAPH y(x)=) Menu
6
&
y(x)= WIND ZOOM TRACE GRAPH
x y INSf DELf SELCT
4
ALL+ ALL
N
STYLE
Chapter 5: Function Graphing
77
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x
Pastes the variable
x
to the current cursor location (same as 2 or - n
ã
X
ä
)
y
Pastes the variable
y
to the current cursor location (same as - n
ã
Y
ä
)
INSf
Inserts a deleted equation variable (function) name above the current cursor location
(only the variable name is inserted)
DELf
Deletes the function that the cursor is on
SELCT
Changes the selection status of the function that the cursor is on (selects or deselects)
ALL+
Selects all defined functions in the equation editor
ALL
N
Deselects all defined functions in the equation editor
STYLE
Assigns the next of seven available graph styles to the function that the cursor is on
Defining a Function in the Equation Editor
Display the equation editor.
If functions are stored in the equation editor,
move the cursor down until a blank function is
displayed.
6 &
( # or
b )
Enter an equation in terms of
x
to define the
function. When you enter the first character,
the function is selected automatically. (The
function’s equals sign is highlighted.)
Move the cursor to the next function.
4
= 2
b or #
To move from the first
equation editor function to
the last, press
$
.
To move to the beginning or
end of an equation, press
-
!
or
-
"
.
An ellipsis indicates that an
equation continues beyond
the screen.
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Notes about Defining Function Equations
You can include functions, variables, constants, matrices, matrix elements, vectors,
vector elements, lists, list elements, complex values, or other equations in the equation.
If you include matrices, vectors, or complex values, the equation must evaluate to a real
number at each point.
You can include another defined function in an equation. For example, given
y1=sin x
and
y2=4+y1
, the function
y2
would equal 4 plus the sine of x.
To enter a function name, select
y
from the equation editor menu, and then enter the
appropriate number.
To insert the contents of an equation variable, use
RCL
(Chapter 1). To enter the
equation variable at the
Rcl
prompt, use the ALPHA keys, alpha keys, and other
character keys.
To select all functions from the home screen or in the program editor, select
FnOn
from
the
CATALOG
(or enter the individual characters) and press
b
.
To select specific functions from the home screen or in the program editor, select
FnOn
from the
CATALOG
(or enter the individual characters), enter the number of each
function, and press
b
. For example, to select
y1
,
y3
, and
y5
, enter
FnOn 1,3,5
.
To deselect functions from the home screen or in the program editor, use
FnOff
the
same way you use
FnOn
to select functions.
When a function evaluates to a non-real number, the value is not plotted on the graph;
no error is returned.
You can edit expressions you
inserted using
Rcl
.
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Selecting Graph Styles
Depending on which graphing mode is set, the TI
-
86 offers up to seven distinct graph styles.
You can assign these styles to specific functions to visually differentiate each from the others.
For example, you can show
y1
as a connected line (
»y1=
in the equation editor) and
y2
as a
dotted line (
Ây2=
), and shade the area above
y3
(
¾y3=
).
Also, you can manipulate the styles to illustrate actual phenomena graphically, such as a ball
flying through the air (using
Á
) or the circular movement of a chair on a Ferris wheel (using
À
).
Icon Style Characteristics of the Plotted Function
»
Line
A solid line connects each plotted point; this is the default in
Connected
mode
¼
Thick
A thick solid line connects each plotted point
¾
Above
Shades the area above the function
¿
Below
Shades the area below the function
À
Path
A circle cursor traces the leading edge of the function and draws a path as it plots
Á
Animate
A circle cursor traces the leading edge of the function as it plots; does not draw a path
Â
Dot
A small dot represents each plotted point; this is the default in
Dot
mode
To set the graph style from a program, select
GrStl(
from the
CATALOG
(A to Z Reference).
The TI
-
86 graphs all selected
functions on the same graph
screen.
¾
(shade above) and
¿
(shade below) are availabl
e
only in
Func
graphing mode.
Â
(dot) is available in all
graphing modes except
DifEq
graphing mode.
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Setting the Graph Style in the Equation Editor
Display the equation editor.
Move the cursor to the function or functions for
which you want to set the graph style.
6 &
#
Display the equation editor menu item
STYLE
.
Select
STYLE
repeatedly to scroll the graph
style icons to the left of the equation name.
/
( (
View the graph with the new graph style.
Clear the
GRAPH
menu to view the graph only.
- *
:
Using Shading Patterns to Differentiate Functions
When you select
¾
(shade above) or
¿
(shade below) for more than one function, the TI
-
86
rotates through a series of four shading patterns.
First shaded function: vertical lines
Second shaded function: horizontal lines
Third shaded function: negatively sloping diagonal lines
Fourth shaded function: positively sloping diagonal lines
The rotation returns to vertical lines for the fifth shaded function and repeats the order.
In the example,
¾
(shade
above) is selected for
y2
. All
window variables are set to
the default values (page 82).
If you assign
¾
or
¿
to a
function that graphs a family
of curves (page 86), the
same pattern rotation applies
to the members of the family
of curves.
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Viewing and Changing On
à
Off Status of Stat Plots
Plot1 Plot2 Plot3
on the top line of the equation editor displays the on
à
off status of each stat
plot (Chapter 14). When a plot name is highlighted on this line, the plot is on.
To change the on
à
off status of a stat plot from the equation editor, press
$
,
"
, and
!
to
place the cursor on
Plot1
,
Plot2
, or
Plot3
, and then press
b
.
Setting the Window Variables
The graph screen window represents the portion of the
coordinate plane displayed on the graph screen. By setting
window variables, you can define the graph screen window
boundaries and other attributes.
xMin
,
xMax
,
yMin
, and
yMax
are the graph screen boundaries.
xScl
(x scale) is the number of units represented by the distance from one tick mark to the next
tick mark on the x-axis.
yScl
(y scale) is the number of units represented by the distance from one tick mark to the
next tick mark on the y-axis.
xRes
sets pixel resolution for function graphs only, using integers
1
through
8
.
At
xRes=1
(the default), functions are evaluated and graphed at each pixel on the x-axis.
At
xRes=8
, functions are evaluated and graphed at every eighth pixel along the x-axis.
To remove tick marks from
both axes, set
xScl=0
and
yScl=0
.
Small
xRes
values improve
graph resolution but may
cause the TI
-
86 to plot
graphs more slowly
.
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Displaying the Window Editor
To display the window editor, select
WIND
from the
GRAPH
menu (
6
'
). Each graphing mode has a unique
window editor. The window editor to the right shows the
default values in
Func
graphing mode.
$
indicates that
xRes=1
(x resolution) is below
yScl
on the window editor.
Changing a Window Variable Value
Display the window editor.
Move the cursor to the window variable you
want to change.
Edit the value, which can be an expression.
Evaluate any expressions and store the value.
6
'
#
#
#
0
b
or
#
To change a window variable value from the home screen or in the program editor, enter
the value, and then press
X
. Either select the window variable from the
VARS
WIND
screen (
-
w
/
/
WIND
) or enter individual characters. Press
b
.
xMin
<
xMax
and
yMin
<
yMax
both must be true to graph
successfully.
In the example,
yMin
is
changed to
0
.
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Setting Graphing Accuracy with
@
x and
@
y
The window variables
@
x
and
@
y
define the distance from the center of one pixel to the
center of any adjacent pixel. When you display a graph, the values of
@
x
and
@
y
are
calculated from
xMin
,
xMax
,
yMin
, and
yMax
using these formulas:
@
x
=(
xMin
+
xMax
)
à
126
@
y
=(
yMin
+
yMax
)
à
62
@
x
and
@
y
are not on the window editor. To change them, you must follow the steps above
for changing a window variable value from the home screen or in the program editor. When
you change the values stored to
@
x
and
@
y
, the TI
-
86 automatically recalculates
xMax
and
yMax
from
@
x
,
xMin
,
@
y
, and
yMin
, and the new values are stored.
Setting the Graph Format
To display the graph format screen, select
FORMT
from the
GRAPH
menu (
6
/
(
). The graph format settings
define various characteristics of the displayed graph. The
current settings are highlighted.
To change a setting, move the cursor onto the new setting,
and then press
b
, the same as on the mode screen.
The TI
-
86 retains
independent format settings
for each graphing mode.
In
DifEq
graphing mode, the
graph format screen key
sequence is
6
/
&
(Chapter 10).
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RectGC
Displays the cursor location as rectangular graph coordinates
x
and
y
; when
RectGC
is set, plotting the graph, moving the free-moving cursor, and tracing update
x
and
y
; if
CoordOn
format also is selected,
x
and
y
are displayed
PolarGC
Displays the cursor location as polar graph coordinates
R
and
q
; when
PolarGC
is set,
plotting the graph, moving the free-moving cursor, and tracing update
x
,
y
,
R
and
q
; if
CoordOn
format also is selected,
R
and
q
are displayed
CoordOn
Displays the cursor coordinates at the bottom of the graph
CoordOff
Does not display the cursor coordinates at the bottom of the graph
DrawLine
Draws a line between the points calculated for the functions in the equation editor
DrawDot
Plots only the calculated points for the functions in the equation editor
SeqG
(sequential graphing) Evaluates and plots one function completely before evaluating
and plotting the next function
SimulG
(simultaneous graphing) Evaluates and plots all selected functions for a single value
of
x
and then evaluates and plots them for the next value of
x
GridOff
Omits the grid points from the display
GridOn
Displays grid points
AxesOn
Displays the axes
AxesOff
Omits the axes from the display;
AxesOff
overrides the
LabelOffàLabelOn
format
setting
LabelOff
Omits the axis labels from the display
LabelOn
Labels the axes, if
AxesOn
is also selected;
x
and
y
for
Func
,
Pol
, and
Param
modes;
various labels in
DifEq
mode
DifEq
graphing mode has a
unique set of graph format
settings (Chapter 10).
Grid points cover the graph
screen in rows that
correspond to the tick marks
on each axis.
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Displaying a Graph
To display a graph, select
GRAPH
from the
GRAPH
menu. The graph
screen is displayed. If the graph is
newly defined, the busy indicator is
displayed at the top-right corner as
the TI
-
86 draws the graph.
In
SeqG
format, the TI
-
86 draws each selected function one by one, in function-name
order (for example,
y1
is graphed first,
y2
is graphed second, and so on).
In
SimulG
format, the TI
-
86 draws all selected graphs simultaneously.
You can display and explore a graph from a program (Chapter 16). To use graphing commands
on the home screen, select them from the
CATALOG
or entering the individual characters.
Pausing or Stopping a Graph in Progress
To pause graph plotting, press
b
. To resume plotting, press
b
again.
To stop graph plotting, press
^
. To replot, select
GRAPH
from the
GRAPH
menu.
Modifying a Drawn Graph
To remove these items from the graph screen: Press (or select):
Cursor, coordinate values, or menus (To restore menus, press
.
or
6
)
:
Free-moving cursor and coordinate values but not the menus
b
Cursor and coordinate values but not the menus
6
or
GRAPH
In the example graph to the
right, all default settings
related to graphing are set.
To view the graph without the
GRAPH
menu on the bottom
line, press
:
after
plotting the graph.
When you pause, the busy
indicator in the top-right
corner becomes a dotted line.
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Graphing a Family of Curves
If you enter a list as an element in an equation, the TI
-
86 plots the function for each value in the
list, graphing a family of curves. In
SimulG
graphing order mode, the TI
-
86 graphs all functions
sequentially for the first element in each list, then for the second element, and so on.
For example,
{2,4,6} sin x
graphs
three functions:
2 sin x
,
4 sin x
, and
6 sin x
.
The equation
{2,4,6} sin ({1,2,3} x)
also graphs three functions:
2 sin x
,
4 sin (2x)
, and
6 sin (3x)
.
Smart Graph
Smart Graph displays the previously displayed graph when you press
6
, as long as all
factors that would cause replotting are unchanged since the graph was last displayed. Smart
Graph replots if you performed any of these actions since the graph was last displayed.
Changed a mode setting that affects graphs
Changed a function or stat plot that was plotted on the last graph screen
Selected or deselected a function or stat plot
Changed the value of a variable in a selected function
Changed the value of a window variable setting
Changed a graph format setting
When you use more than one
list in an expression, all lists
must have the same
dimension.
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Graph Tools on the TI
-
86................................................... 88
Tracing a Graph ................................................................. 90
Resizing the Graph Screen with ZOOM Operations ........... 91
Using Interactive Math Functions ...................................... 95
Evaluating a Function for a Specified x............................ 101
Drawing on a Graph ........................................................ 101
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
6
Graph Tools
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Graph Tools on the TI-86
Chapter 5 describes how to use the
GRAPH
menu items
y(x)=
,
WIND
,
GRAPH
, and
FORMT
to
define and display the graph of a function in
Func
graphing mode. This chapter describes how
to use the other
GRAPH
menu items to apply preset graph screen dimensions, explore the
graph and trace specific functions, perform mathematical analyses, draw on graphs, and store
and recall graphs and drawings. You can use most graph tools in all four graphing modes.
The GRAPH Menu
6
y(x)= WIND ZOOM TRACE GRAPH
4
MATH DRAW FORMT STGDB RCGDB
4
EVAL STPIC RCPIC
ZOOM
Displays the
GRAPH
ZOOM
menu; use these items to apply preset graph screen dimensions
TRACE
Activates the trace cursor; use this cursor to trace along graphs of specific functions
MATH
Displays the
GRAPH
MATH
menu; use this menu to explore graphs mathematically
DRAW
Displays the
GRAPH
DRAW
menu; use this menu to draw on graphs
STGDB
Displays the
Name=
prompt and
GDB
menu; use this prompt to enter a
GDB
variable
RCGDB
Displays the
Name=
prompt and
GDB
menu; use this menu to recall a
GDB
variable
EVAL
Displays the
Eval
x=
prompt; use this prompt to enter an
x
value for which you want to
solve the current function
STPIC
Displays the
Name=
prompt and
PIC
menu; use this prompt to enter a
PIC
variable
RCPIC
Displays the
Name=
prompt and
PIC
menu; use this menu to recall
PIC
variable
This is the
GRAPH
menu in
Func
graphing mode. The
GRAPH
menu differs slightly
from graphing mode to
graphing mode.
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Using the Free-Moving Cursor
When you select
GRAPH
from the
GRAPH
menu, the graph
screen is displayed with the free-moving cursor at the
center of the screen.
The cursor appears as a plus sign with a flashing center
pixel. To move the cursor, press
"
,
#
,
!
, or
$
; it moves
in the direction of the cursor key you press.
In
RectGC
format, each cursor movement updates the variables
x
and
y
. In
PolarGC
format, each cursor movement updates
x
,
y
,
R
, and
q
.
In
CoordOn
format, the
x
and
y
cursor coordinates are displayed at the bottom of the
graph screen as you move the cursor.
Graphing Accuracy
The coordinate values displayed as you move the cursor approximate actual mathematical
coordinates, accurate to within the width and height of the pixel. As the difference between
xMin
and
xMax
and between
yMin
and
yMax
becomes smaller (for example, when you zoom
in on a graph), graphing is more accurate and coordinate values approximate the actual
mathematical coordinates more closely.
The free-moving cursor coordinates represent the cursor location on the graph screen.
Moving the free-moving cursor precisely from one plotted point to the next along a function
is very difficult. To move along a function easily, use the trace cursor (page 90).
In the example, the function
y(x)=x^3+.3x
2
-4x
is graphed.
The numeric display mode
settings do not affect
coordinate display.
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Tracing a Graph
To display the graph and begin a trace, select
TRACE
from the
GRAPH
menu.
The trace cursor appears as a small square with a flashing
diagonal line at each corner. Initially, the trace cursor
appears on the first selected function, at the
x
value
closest to the middle of the screen.
If
CoordOn
format is selected, the cursor coordinates are
displayed at the bottom of the screen.
To move the trace cursor... Press these keys:
To the next larger or next smaller plotted point in a function
"
or
!
To any valid independent-variable value (
x
,
q
, or
t
) on the current equation
value
b
From one function to another function at
x
, in the order or reverse order of
the selected functions in the equation editor
#
or
$
From one member to another member of a family of curves (Chapter 5)
#
or
$
As you move the trace cursor along a function, the
y
value is calculated from the
x
value. That is,
y=y
n
(x)
. When you trace beyond the top or bottom of the graph screen, the coordinates
displayed on the screen continue to change as if the cursor were still on the screen.
Panning:
To view function coordinates to the left or right of the current graph screen,
press and hold
!
or
"
while tracing. When you pan beyond the left or right side of the
screen during a trace, the TI
-
86 automatically changes the values of
xMin
and
xMax
.
In the example, the function
y(x)=x^3+.3x
2
-4x
is graphed.
When you enter the first
character of an independent
variable value, an
x=
prompt
is displayed (or
q
=
or
t=
). The
value can be an expression.
If the function is undefined at
an
x
value, then the
y
value
is blank.
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Quick Zoom:
While tracing, you can press
b
to adjust the graph screen so that the
trace cursor location becomes the center of a new graph screen, even if you have moved
the cursor beyond the top or bottom of the display. In effect, this is vertical panning.
Stopping and Resuming a Trace
To stop tracing and restore the free-moving cursor, press
:
or
6
.
To resume tracing, select
TRACE
from the
GRAPH
menu. If Smart Graph has not replotted
the graph (Chapter 5), the trace cursor is at the point where you stopped tracing.
Resizing the Graph Screen with ZOOM Operations
The standard TI
-
86 graph screen displays the portion of the xy plane defined by the values
stored to the window variables. With the
GRAPH
ZOOM
menu items, you can change some
or all of the window variable values and redisplay the graph, usually with one keystroke. As
a result, a smaller or larger portion of the xy plane is displayed.
The GRAPH ZOOM Menu
6
(
y(x)= WIND ZOOM TRACE GRAPH
BOX ZIN ZOUT ZSTD ZPREV
4
ZFIT ZSQR ZTRIG ZDECM ZDATA
4
ZRCL ZFACT ZOOMX ZOOMY ZINT
4
ZSTO
To view the current window
variable values, select
WIND
from the
GRAPH
menu.
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BOX
Draws a box to define the graph screen
ZIN
(zoom in) Magnifies the graph around the cursor by factors of
xFact
and
yFact
ZOUT
(zoom out) Displays more of the graph around the cursor by factors of
xFact
and
yFact
ZSTD
Displays the graph in standard dimensions; resets the default window variable values
ZPREV
Reverses the last zoom operation; window variables revert to previous values
ZFIT
Recalculates
yMin
and
yMax
to include the minimum and maximum
y
values of the
selected functions between the current
xMin
and
xMax
ZSQR
Sets equal-size pixels on the x-axis and y-axis; adjusts window variable values in one
direction so that
@
x=
@
y
, while
xScl
and
yScl
remain unchanged; the midpoint of the
current graph (not the axes intersection) becomes the midpoint of the new graph
ZTRIG
Sets built-in window variables appropriate for trigonometric functions in
Radian
mode:
xMin=
L
8.24668071567 xScl=1.5707963267949
(
p
à
2)
yMax=4
xMax=8.24668071567 yMin=
L
4 yScl=1
ZDECM
Sets
@
x=.1
,
@
y=.1
,
xMin=
L
6.3
,
xMax=6.3
,
xScl=1
,
yMin=
L
3.1
,
yMax=3.1
, and
yScl=1
ZDATA
Sets window variable values to display all statistical data points; adjusts
xMin
and
xMax
only; applies to histograms, scatter plots, and stat plots only (Chapter 14)
ZRCL
Uses window variable values stored in the user-defined zoom-window variables (
ZSTO
)
ZFACT
Displays the
ZOOM
FACTORS
screen
ZOOMX
Zooms out by a factor of
xFact
only; ignores
yFact
(page 93)
ZOOMY
Zooms out by a factor of
yFact
only; ignores
xFact
ZINT
Sets integer values on the axes; sets
@
x=1
,
@
y=1
,
xScl=10
, and
yScl=10
; the current
cursor becomes the center of the new graph screen after you press b
ZSTO
Stores current window variable values to user-defined zoom-window variables (
ZRCL
)
To cancel the effect of any
ZOOM
menu item and return
to the default window variabl
e
values, select
ZSTD
.
If you graph a circle but it
appears elliptical, you can
use
ZSQR
to reset the
window variable values so
that the circle graph appears
circular.
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Defining a Custom Zoom In
Using
BOX
, you can zoom in on any rectangular area within the current graph screen.
Select
BOX
from the
GRAPH
ZOOM
menu. The
zoom cursor is displayed at center screen.
Move the cursor to any spot you want to define
as a corner of the zoom box; mark the corner
with a small square.
6
(
&
"
#
!
$
b
Move the cursor away from the first corner,
creating an adjustable box whose diagonal
corners are the small square and the cursor.
When you have defined the box, replot all
selected functions in the new graph screen.
Clear the menus from the screen.
"
#
!
$
b
:
Setting Zoom Factors
Zoom factors define the magnification or reduction factor by which
ZIN
,
ZOUT
,
ZOOMX
, and
ZOOMY
zoom in or zoom out around a point. To display the zoom factors editor, select
ZFACT
from the
GRAPH
ZOOM
menu (press
6
(
/
/
'
).
xFact
and
yFact
must
be
1. The default value for both factors is
4
in all graphing modes.
Zooming In and Zooming Out on a Graph
ZIN
magnifies the part of the graph surrounding the cursor location.
ZOUT
displays a greater
portion of the graph, centered on the cursor location.
xFact
and
yFact
determine the extent.
The steps below describe how to use
ZIN
. To use
ZOUT
, select it instead of
ZIN
in step 2.
Before you begin these
steps, enter a function in the
equation editor. In the
example, the function
y(x)=x^3+.3x
2
N
4x
is graphed.
To cancel
BOX
without
redefining the graph screen,
press
:
.
When you replot the graph,
the TI
-
86 updates the windo
w
variable values.
To store to
xFact
or
yFact
from the home screen or in
the program editor, you can
select it from the
VARS ALL
screen or enter it using
ALPHA and alpha keys.
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Check
xFact
and
yFact
; change as needed. 6 (
/ /
'
Select
ZIN
from the
GRAPH
ZOOM
menu to
display the zoom cursor.
Move the zoom cursor to the intended new
center point of the graph screen.
( '
" # ! $
Zoom in. The TI
-
86 adjusts the graph screen by
xFact
and
yFact
, updates window variable
values, and replots the selected functions
centered on the cursor location.
b
You can continue to zoom in (or zoom out) on the current graph, unless you press a key
other than
b
,
"
,
#
,
!
, or
$
.
To zoom in (or zoom out) again at the same point, press
b
.
To zoom in (or zoom out) at a new center point, move the cursor and press
b
.
To zoom out only on the horizontal axis by a factor of
xFact
, select
ZOOMX
instead of
ZIN
in
step 2 above.
ZOOMX
plots the selected functions centered on the cursor location and
updates some window variable values;
yMin
and
yMax
are unchanged.
To zoom out only on the vertical axis by a factor of
yFact
, select
ZOOMY
instead of
ZIN
in
step 2 above.
ZOOMY
plots the selected functions centered on the cursor location and
updates some window variable values;
xMin
and
xMax
are unchanged.
In the example, the function
y(x)=x^3+.3x
2
N
4x
is graphed.
When you select a
ZOOM
feature, Smart Graph
displays the current graph.
To cancel a zoom before you
complete it, press
:
.
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Storing and Recalling Zoom-Window Variable Values
To store all current zoom-window variable values simultaneously as a user-defined
custom zoom feature, select
ZSTO
from the
GRAPH
ZOOM
menu.
To execute a user-defined custom zoom, which resets the graph screen to the stored
zoom-window variables, select
ZRCL
from the
GRAPH
ZOOM
menu.
Using
ZSTO
in these graphing modes: Stores to these zoom-window variables:
Func
,
Pol
,
Param
, and
DifEq
graphing modes
zxMin
,
zxMax
,
zxScl
,
zyMin
,
zyMax
, and
zyScl
Pol
graphing mode only
z
q
Min
,
z
q
Max
, and
z
q
Step
Param
graphing mode only
ztMin
,
ztMax
, and
ztStep
DifEq
graphing mode only
ztMin
,
ztMax
,
ztStep
, and
ztPlot
Using Interactive Math Functions
When you select a
GRAPH
MATH
operation, Smart Graph displays the current graph with the
trace cursor. To perform the
GRAPH
MATH
operation, press
#
and
$
to move to the function.
When a
GRAPH
MATH
menu operation prompts you to specify left bound, right bound, and
guess, the accuracy of the values you specify will affect the length of time the TI
-
86 spends
calculating the answer; the better the guess, the shorter the calculation time.
The GRAPH MATH Menu
6
/
&
MATH DRAW FORMT STGDB RCGDB
ROOT dy
à
dx
f(x) FMIN FMAX
4
INFLC YICPT ISECT DIST ARC
4
TANLN
You can select all zoom-
window variables from the
VARS WIND
screen in any
graph mode.
You also can enter the
variable characters
individually.
The zoom-window variables
resume their standard default
values when you reset
defaults.
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ROOT
Finds the root of a function using a specified left bound, right bound, and guess
dy
à
dx
Finds a numeric derivative (slope) of a function at the trace cursor location
f(x)
Finds a function’s numerical integral using a specified left bounds and right bound
FMIN
Finds a function’s minimum using a specified left bound, right bound, and guess
FMAX
Finds a function’s maximum using a specified left bound, right bound, and guess
INFLC
Finds a function’s inflection point using a specified left bound, right bound, and guess
YICPT
Finds a function’s y-intercept (
y
at
x=0
)
ISECT
Finds the intersection of two functions using a specified left bound, right bound, and guess
DIST
Finds the straight-line distance between a specified left bound and right bound
ARC
Finds the distance along a function between two specified points on the function
TANLN
Draws the tangent line at a specified point
Settings That Affect GRAPH MATH Operations
The tolerance variable
tol
(Appendix) affects the accuracy of
f(x)
,
FMIN
,
FMAX
, and
ARC
.
Accuracy increases as the tolerance value becomes smaller.
The step-size variable
d
(Appendix) affects the accuracy of
dy
à
dx
,
INFLC
in
dxNDer
differentiation mode (Chapter 1),
ARC
, and
TANLN
. Accuracy increases as the step-size
value becomes smaller.
The differentiation mode setting affects
dy
à
dx
,
INFLC
,
ARC
, and
TANLN
;
dxDer1
(exact)
mode is more accurate than
dxNDer
(numeric) mode (Chapter 1).
The
GRAPH
MATH
menu
differs slightly for
Pol
and
Param
graphing modes
(Chapters 8 and 9).
DifEq
graphing mode has no
GRAPH
MATH
menu.
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Using ROOT, FMIN, FMAX, or INFLC
The steps for
ROOT
,
FMIN
,
FMAX
, and
INFLC
are the same, except for the menu selection in step 1.
Select
ROOT
from the
GRAPH
MATH
menu.
A
Left Bound?
prompt is displayed.
Move the cursor onto the function for which
you want to find a root.
6
/
&
&
#
$
Specify the left bound for
x
. Either move the
trace cursor to the left bound or enter a
value directly.
Right Bound?
is displayed.
a
3
b
(or
!
"
b
)
Specify the right bound for
x
as in step 3.
Guess?
is displayed.
Guess an
x
value near the root between the
left bound and the right bound. Either move
the cursor or enter a value.
a
1
b
(or
!
"
b
)
!
"
(or
a
2
)
Solve for
x
. The result cursor is displayed at
the solution point, the cursor coordinate
values are displayed, and the
x
value is
stored in
Ans
.
b
In the example, the function
y(x)=x^3+.3x
2
N
4x
is selected.
Step 2 is not necessary here
because only one function is
selected.
When you enter a value
directly for the left bound,
right bound, or guess, an
x=
prompt is displayed on the
bottom of the graph screen.
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Using
f(x), DIST, or ARC
The steps for using
f(x)
,
DIST
, and
ARC
are the same, except for the menu selection in step 1.
Select
DIST
from the
GRAPH
MATH
menu.
The current graph is displayed with a
Left
Bound?
prompt.
Move the cursor onto the function on which
the left bound is a point.
6
/
&
/
)
#
$
Select the left bound for
x
. Either move the
cursor to the left bound or enter the
x
value.
Right Bound?
is displayed.
!
"
b
or
value
b
(
DIST
only) If you want the right bound to be
a point on another function, move the cursor
to the other function.
Select the right bound. Either move the
cursor to the right bound or enter its
x
value.
#
$
!
"
or
value
Solve.
For
DIST
, the solution
DIST=
is displayed
and stored in
Ans
.
For
ARC
, the solution
ARC=
is displayed
and stored in
Ans
.
For
f(x)
, the solution
f(x)=
is displayed,
b
shaded, and stored in
Ans
. The function integral error value is stored to the variable
fnIntErr
(Appendix). To remove the shading, select
CLDRW
from the
GRAPH DRAW
menu (page 103).
In the example, the function
y(x)=x^3+.3x
2
N
4x
is selected.
Steps 2 and 4 are not
necessary here because only
one function is selected.
For
DIST
, when you are
specifying the right bound, a
line is drawn from the left
bound to the right bound.
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Using dy
à
dx or TANLN
The steps for using
dy
à
dx
and
TANLN
are the same, except for the menu selection in step 1.
Select
dy
à
dx
from the
GRAPH
MATH
menu.
The current graph is displayed.
Move the cursor to the function with the point for
which you want to find the derivative, or slope.
6
/
&
'
#
$
Move the cursor to the point (or enter the
x
value).
Solve.
For
dy
à
dx
, the solution
dy
à
dx=
is displayed
and stored in
Ans
.
For
TANLN
, a tangent line also is displayed.
!
"
b
To remove the tangent line and
dy
à
dx=
prompt, select
CLDRW
from the
GRAPH
DRAW
menu.
In the example, the function
y(x)=x^3+.3x
2
N
4x
is selected.
TANLN
(
GRAPH
MATH
menu
)
and
TanLn
(
GRAPH
DRAW
menu) both draw a tangent
line on the graph; only
TANLN
displays the solution,
dy
à
dx
.
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Using ISECT
Select
ISECT
from the
GRAPH
MATH
menu.
The current graph is displayed with
First Curve?
at the bottom of the graph screen.
Select the first function (curve). The cursor
moves to the next function and
Second Curve?
is displayed.
6 /
& / (
# $ b
Select the second function (curve).
Guess?
is
displayed.
Guess the intersection. Either move the cursor to
a point near an intersection or enter an
x
value.
# $ b
a
1
`
5
(or ! ")
Solve. The result cursor is displayed at the
intersection , the cursor coordinates are the
result, and the
x
value is stored to
Ans
.
b
Using YICPT
To use
YICPT
, select
YICPT
from the
GRAPH
MATH
menu (
6
/
&
/
'
). Press
#
and
$
to select a function, and then press
b
. The result cursor is displayed at the
y-intercept, the cursor coordinate values are displayed, and
y
is stored in
Ans
.
In the example, the functions
y(x)=x^3+.3x
2
N
4x
and
y(x)=x
2
+3x
N
3
are selected.
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Evaluating a Function for a Specified x
Select
EVAL
from the
GRAPH
menu. The
graph is displayed with the
Eval x=
prompt in
the bottom-left corner.
Enter a real
x
value between window
variables
xMin
and
xMax
.
6 /
/ &
`
5
- ~
Evaluate. The result cursor is on the first
selected function at the entered
x
value. The
coordinate values are displayed. The number
in the top-right corner indicates which
function is evaluated.
b
Move the result cursor to the next or previous
selected function. The result cursor is on the
next or previous function at entered
x
value,
the coordinate values are displayed, and the
function number changes.
$ #
Drawing on a Graph
You can use the drawing tools (except
DrInv
) to draw points, lines, circles, shaded areas,
and text on the current graph in any graphing mode. The drawing tools use the display’s x-
and y-coordinate values.
To clear entered numbers
from the
Eval x=
prompt,
press
:
.
To cancel
EVAL
, press
:
after clearing the
Eval x=
prompt.
Expressions are valid for
x
.
You may continue to enter
valid
x
values for which to
evaluate the selected
functions.
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Before Drawing on a Graph
All drawings are temporary; they are not stored in a graph database. Any action that causes
Smart Graph to replot the graph erases all drawings. Therefore, before you use any drawing
tool, consider whether you want to perform any of these graphing activities first.
Change a mode setting that affects graphs
Select, deselect, or edit a current function or stat plot
Change the value of a variable used in a selected function
Change a window variable value
Change a graph format setting or graph style
Clear current drawings with
CLDRW
Saving and Recalling Drawn Pictures
To store the elements that define the current graph to a graph database (
GDB
) variable,
select
STGDB
from the
GRAPH
menu. These information types are stored to a
GDB
variable:
Equation editor functions
Window variable values
Graph style settings
Format settings
To recall the stored
GDB
later, select
RCGDB
from the
GRAPH
menu, and then select the
GDB
variable from the
GRAPH
RCGDB
menu. When you recall a
GDB
, the information stored
in the
GDB
replaces any current information of these types.
To store the current graph display, including drawings, to a picture (
PIC
) variable, select
STPIC
from the
GRAPH
menu. Only the graph picture is stored to the specified
PIC
variable.
To superimpose one or more stored graph pictures onto a graph later, select
RCPIC
from the
GRAPH
menu, and then select the
PIC
variable from the
GRAPH
RCPIC
menu.
Graph database (GDB) and
picture (PIC) variable names
can be from one to eight
characters long. The first
character must be a letter.
The next section describes
how to draw lines, points,
curves, and text onto a
graph; you then can store the
drawings to a
PIC
variable.
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Clearing Drawn Pictures
To clear drawn pictures while the graph is displayed, select
CLDRW
from the
GRAPH
DRAW
menu. The graph is replotted and displayed with no drawn elements.
To clear drawn pictures from the home screen, select
ClDrw
from the
CATALOG
.
ClDrw
is
pasted to the cursor location. Press
b
.
Done
is displayed; when you display the graph
again, no drawings are displayed.
The GRAPH DRAW Menu
6
/
'
MATH DRAW FORMT STGDB RCGDB
Shade LINE VERT HORIZ CIRCL
4
DrawF PEN PTON PTOFF PTCHG
4
CLDRW PxOn PxOff PxChg PxTest
4
TEXT TanLn DrInv
You can use these
GRAPH
DRAW
menu items only on the home screen or in the program editor.
Shade(
Shades a specified area of a graph (See page 104)
DrawF expression
Draws
expression
as a function
PxOn(row,column)
Turns on the pixel at
(row,column)
PxOff(row,column)
Turns off the pixel at
(row,column)
PxChg(row,column)
Changes the on
à
off status of the pixel at
(row,column)
PxTest(row,column)
Returns
1
if the pixel at
(row,column)
is on, or
0
if the pixel is off
TanLn(expression,x)
Draws
expression
as a function and a tangent line of
expression
at
x
DrInv expression
Draws the inverse of
expression
DrInv
is not available in
Pol
,
Param
, or
DifEq
graphing
modes.
For
PxOn
,
PxOff
,
PxChg
, and
PxTest
,
row
and
column
are
integers, where
0
row
62
and
0
column
126
.
For
DrawF
,
TanLn
, and
DrInv
,
expression
is in terms
of
x
. Also, you cannot include
a list in
expression
to draw a
family of curves.
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Shading Areas of a Graph
To shade an area of a graph, the syntax is:
Shade(
lowerFunc
,
upperFunc
ã
,
xLeft
,
xRight
,
pattern
,
patternRes
ä
)
pattern
specifies one of four shading patterns.
1
vertical (default)
2
horizontal
3
negative slope( 45
¡
)
4
positive slope (45
¡
)
patternRes
specifies one of eight shading resolutions.
1
every pixel (default)
2
every second pixel
3
every third pixel
4
every fourth pixel
5
every fifth pixel
6
every sixth pixel
7
every seventh pixel
8
every eighth pixel
The area that is specifically above
lowerFunc
and below
upperFunc
is shaded.
xLeft
>
xMin
and
xRight
<
xMax
must be true.
xLeft
and
xRight
specify left and right bounds for shading. (
xMin
and
xMax
are defaults.)
These
GRAPH
DRAW
menu items are interactive. Also, you can use all of them, except
PEN
,
on the home screen or in a program (A to Z Reference).
LINE
Draws a line segment from one point to another point you specify with the cursor
VERT
Draws a vertical line, which you can move to any displayed
x
value
To replicate the example
without additional graphs,
turn off all equations and stat
plots before entering the
instructions as shown.
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HORIZ
Draws a horizontal line, which you can move to any displayed
y
value
CIRCL
Draws a circle with a center point and radius you specify with the cursor
PEN
Draws the path of the cursor as you move it on the graph screen
PTON
Turns on the point at the cursor location
PTOFF
Turns off the point at the cursor location
PTCHG
Changes the on
à
off status of a point at the cursor location
CLDRW
Clears all drawings from the graph screen; replots the graph
TEXT
Draws characters on the graph at the cursor location
Drawing a Line Segment
Select
LINE
from the
GRAPH
DRAW
menu. The
graph is displayed.
Define one segment endpoint with the cursor.
6 /
' '
" # ! $
b
Define the other endpoint of the segment. As
you move the cursor, a line anchored at the
first defined endpoint extends to the cursor.
Draw the line.
" # ! $
b
To draw more line segments, repeat steps 2 and 3; to cancel
LINE
, press
:
.
In the example, the functions
y(x)=x^3+.3x2
N
4x
and
y(x)=x2+3x
N
3
are selected.
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Drawing a Vertical or Horizontal Line
Select
VERT
(or
HORIZ
) from the
GRAPH
DRAW
menu. The graph is displayed and a
vertical or horizontal line is drawn at the cursor.
6 /
' (
(or ))
Move the line to the
x
value (or to the
y
value,
if horizontal) through which you want the line
to pass.
Draw the line on the graph.
! "
(or $ #)
b
To draw more lines, repeat steps 2 and 3; to cancel
VERT
or
HORIZ
, press
:
.
Drawing a Circle
Select
CIRCL
from the
GRAPH
DRAW
menu. The graph is displayed.
Define the center point of the circle with
the cursor.
6 / '
*
" # ! $
b
Move the cursor to any point on the
intended circumference.
Draw the circle.
" # ! $
b
To draw more circles, repeat steps 2 through 4; to cancel
CIRCL
, press
:
.
In the example, the function
y(x)=x^3+.3x
2
N
4x
is selected.
Also,
ZIN
was executed once
with the zoom cursor at (0,0),
xFact=2
, and
yFact=2
.
In the example, the function
y(x)=x^3+.3x
2
N
4x
is selected.
Also,
ZIN
was executed once
with the zoom cursor at (0,0),
xFact=2
, and
yFact=2
.
Here the circle appears as a
circle, regardless of window
variable values. When you
use
Circl(
from the
CATALOG
to draw a circle, the current
window variable values may
distort the shape.
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Drawing a Function, Tangent Line, or Inverse Function
For
DrawF
,
TanLn
, and
DrInv
,
expression
is in terms of
x
. When you select
DrawF
,
TanLn
, or
DrInv
from the
GRAPH
DRAW
menu, it is pasted to the home screen or program editor. Upon
execution, the drawing is returned.
DrInv
draws the inverse of
expression
by plotting its
x
values on the y-axis and its
y
values on the x-axis.
DrInv
is available only in
Func
graphing mode.
DrawF
expression
TanLn(
expression
,
x
) DrInv
expression
DrawF x^3+.3x
2
+4x TanLn(y1,1.5) DrInv y1
Drawing Freehand Points, Lines, and Curves
Select
PEN
from the
GRAPH
DRAW
menu.
6
/
'
/
'
Move the cursor to where you want to
begin drawing.
Turn on the pen.
Draw whatever you want.
Turn off the pen.
"
#
!
$
b
"
#
!
$
b
To draw more points, lines, or curves, repeat steps 2 through 5. To cancel, press
:
.
For
DrawF
,
TanLn
, and
DrInv
, you can use as
expression
any variable to
which a valid expression is
stored (including deselected
equation variables).
In the illustrations,
y1=x^3+.3x
2
N
4x
is selected.
In the example, the function
y(x)=x^3+.3x
2
N
4x
is selected.
Also,
ZSTD
was executed.
To draw a diagonal line or
curve, turn on the pen, press
b
b
, press
!
$
(or
#
"
, and so on), and repeat.
108
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Placing Text on a Graph
Select
TEXT
from the
GRAPH
DRAW
menu.
The text cursor is displayed.
Move the cursor to where you want to enter
text. Text is entered below the text cursor.
6/ '
/ / /
&
" # ! $
Set alpha-lock and enter
min
. (The alpha
cursor ( Ï ) is displayed in the top-right
corner.
Move the cursor to another location.
Enter
max
(alpha-lock remains on).
- n 1
ã
M
ä
ã
I
ä
ã
N
ä
" # ! $
ã
M
ä
ã
A
ä
ã
X
ä
Turning On or Turning Off Points
Select
PTON
(or
PTOFF
) from the
GRAPH
DRAW
menu.
Move the cursor to where you want to draw
(or erase) a point.
Turn on (or turn off) the point.
6 / '
/ (
" # ! $
b
To continue drawing points, repeat steps 2 and 3. To cancel
PTON
, press
:
.
This example adds to the
PEN
example drawing.
Before you start, you may
want to store the arrows to a
picture variable (page 102).
To erase a character when
using
TEXT
, move the
TEXT
cursor above it and then
press
1
¤
or
-
n
¤
to overwrite it.
In the example, the function
y(x)=x^3+.3x
2
N
4x
is selected.
Also,
ZSTD
was executed.
Points are turned on at (
L
5,5),
(5,5), (5,
L
5), and (
L
5,
L
5).
07TABLES.DOC TI-86, Chap 7, US English Bob Fedorisko Revised: 02/13/01 2:25 PM Printed: 02/13/01 3:02 PM Page 109 of 6
Displaying the Table ........................................................110
Setting Up the Table ........................................................ 113
Clearing the Table............................................................ 114
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Tables
7
110
Chapter 7: Tables
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Displaying the Table
The table displays the independent values and corresponding dependent values for up to 99
selected functions in the equation editor. Each dependent variable in the table represents a
selected function stored in the equation editor for the current graphing mode.
TABLE Menu
7
TABLE TBLST
table screen
table setup editor
The Table
7
&
independent variable values dependent (equation) variable values
variable names
edit line (function name and
full value of current cell shown)
current cell
table menu
To edit an equation, press
$
in the equation’s table column until the cursor highlights the
equation variable on the top line, and then press
b
. The expression stored to the
current equation variable is displayed in the edit line.
To display the equation
editor, press
6
&
(Chapter 5).
In the example,
y1=x
2
+3x-4
and
y2=sin (3x)
are selected
and all defaults set.
The table abbreviates values
in the columns, if necessary.
Chapter 7: Tables
111
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Independent and Dependent Variables in the Table
Graphing Mode Independent Variable Dependent (Equation) Variables
Func
(function)
xy1
through
y99
Pol
(polar)
q
r1
through
r99
Param
(parametric)
t xt1àyt1
through
xt99àyt99
DifEq
(differential equation)
tQ1
through
Q9
Navigating the Table
To... Do this:
Display more dependent variables in the table Press " or !
Display greater values in any column Press # (only when
Indpnt: Auto
is set; page 112)
Set
TblStart
to a lower value Press $ in the independent variable column until the
cursor moves past the current
TblStart
(page 112)
Display the equation in the edit line, where you
can edit or deselect it
Press ! or " to move the cursor to an equation
v
ariable column, hold $ until the cursor highlights
the equation name, and then press b; the
equation is displayed in the edit line
In
DifEq
mode, if an equation
has an initial conditions list,
the table uses the first list
element to evaluate the
equation (Chapter 10).
112
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The Table Menus
7
&
The table has a unique menu for each graphing mode, as shown below.
In Function Graphing Mode In Parametric Graphing Mode
TBLST SELCT x y TBLST SELCT t xt yt
In Polar Graphing Mode In Differential Equation Graphing Mode
TBLST SELCT
q
r TBLST SELCT t Q
TBLST
Displays the table setup editor
SELCT
On the edit line, deselects or cancels deselection of the equation
x
and
y
;
q
and
r
;
t
,
xt
,
and
yt
; or
t
and
Q
On the edit line, pastes the variable to the cursor location; the variables
change according to graphing mode
To add an equation to the table, select it in the equation editor (Chapter 5).
SELCT
only
removes equations from the table.
To remove an equation from a column in the table, select
SELCT
from the table menu.
Remaining equations that follow the removed equation shift left one column.
To deselect an equation with
SELCT
, the equation and cursor must be displayed in the
edit line. If the equation is in the edit line but the cursor is not, press
b
.
To compare two dependent variables not defined consecutively in the equation editor,
use
SELCT
from the table screen menu to deselect the dependent variables in between.
Chapter 7: Tables
113
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Setting Up the Table
To display the table setup editor, select
TBLST
from the
TABLE
menu. The screen to the right shows the default
table setup settings.
TblStart
specifies the first independent variable value (
x
,
q
,
or
t
) in the table (only when
Indpnt: Auto
is selected).
@
Tbl
(table step) specifies the increment or decrement from one independent variable value
to the next independent variable value in the table.
If
@
Tbl
is positive, then the values of
x
,
q
, or
t
increase as you scroll down the table.
If
@
Tbl
is negative, then the values of
x
,
q
, or
t
decrease as you scroll down the table.
Indpnt: Auto
displays independent variable values automatically in the first column of the table,
starting at
TblStart
.
Indpnt: Ask
displays an empty table. As you enter
x
values in the
x=
prompt (
x=
value
b
),
each value is added to the independent variable column and the corresponding dependent
variable values are calculated and displayed. When
Ask
is set, you cannot scroll beyond the six
independent variable values that are currently displayed in the table.
To display the table using the
current table setup settings,
select
TABLE
from the
TABLE
menu.
TblStart
and
@
Tbl
must be
real numbers; you can enter
an expression.
In
DifEq
graphing mode,
it is a good practice to set
TblStart
=
tMin
and
@
Tbl
=
tStep
.
114
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Viewing and Editing Dependent Variable Equations
Display the table.
Move the cursor into the column of the
dependent variable you want to edit, and
then move up the column until the name is
highlighted.
7 &
" $
Display the equation in the edit line. b
Edit the equation.
Enter the edited equation.
The dependent variable values are
recalculated.
" " "
5
"
\
1
b
The cursor returns to the edited dependent variable’s first value.
The equation editor is updated.
Clearing the Table
To clear the table when
Indpnt: Ask
is set, select
ClTbl
from the
CATALOG
, and then press
b
. All independent and dependent variable columns are cleared.
ClTbl
does nothing
when
Indpnt: Auto
is set.
In the example,
y1=x
2
+3x-4
and
y2=sin (3x)
are selected
and all defaults set.
When you display the
equation in the edit line, the
column equation name is
highlighted.
When you use
ClTbl
in a
program, the table is cleared
upon program execution
(Chapter 16).
08POL.DOC TI-86, Chap 8, US English Bob Fedorisko Revised: 02/13/01 2:26 PM Printed: 02/13/01 3:02 PM Page 115 of 8
Preview: Polar Graphing .................................................. 116
Defining a Polar Graph .................................................... 117
Using Graph Tools in Pol Graphing Mode........................ 119
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Polar Graphing
8
116
Chapter 8: Polar Graphing
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Preview: Polar Graphing
The graph of the polar equation A sin (B
q
) forms the shape of a flower. Graph the flower for
A=8 and B=2.5. Then explore the appearance of the flower for other values of A and B.
Select
Pol
mode from the mode screen.
-
m
#
#
#
#
"
b
Display the equation editor and polar
equation editor menu.
(Deselect or delete all equations if any.)
Store
r1(
q
)=8sin(2.5
q
)
.
6
&
(
/
'
/
)
8
=
D
2
`
5
&
E
Select
ZSTD
from the
GRAPH
ZOOM
menu.
r1
is plotted on the graph screen.
-
g
)
Display the window editor, and then
change
q
Max
to
4
p
.
'
#
4
-
~
Select
ZSQR
from the
GRAPH
ZOOM
menu.
xMin
and
xMax
are changed to
display the graph in correct proportion.
Change the values of A and B and
redisplay the graph.
(
/
'
&
(enter other A
and B values)
To remove the
GRAPH
menu
from the graph screen, as
shown, press
:
.
To redisplay the
GRAPH
menu, press
6
.
Chapter 8: Polar Graphing
117
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Defining a Polar Graph
The steps for defining a polar graph are similar to the steps for defining a function graph. This
chapter assumes that you are familiar with Chapter 5: Function Graphing and Chapter 6:
Graph Tools. Chapter 8 details aspects of polar graphing that differ from function graphing.
Setting Polar Graphing Mode
To display the mode screen, press
-
m
. To graph polar equations, you must select
Pol
graphing mode before you enter equations, set the format, or edit window variable values. The
TI
-
86 retains separate equation, format, and window data for each graphing mode.
The GRAPH Menu
6
r(
q
)= WIND ZOOM TRACE GRAPH
4
MATH DRAW FORMT STGDB RCGDB
4
EVAL STPIC RCPIC
polar polar polar
equation window graph math
editor editor menu
Chapter 5 describes these
GRAPH
menu items:
GRAPH
and
FORMT
.
Chapter 6 describes these
GRAPH
menu items:
ZOOM
,
TRACE
,
DRAW
,
STGDB
,
RCGDB
,
EVAL
,
STPIC
, and
RCPIC
.
118
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Displaying the Polar Equation Editor
To display the polar equation editor, select
r(
q
)=
from the
GRAPH
menu in
Pol
graphing mode
(
6
&
). The polar equation editor menu displayed on the bottom line is the same as the
Func
mode equation editor menu, except that
q
and
r
replace
x
and
y
.
In this editor, you can enter and display up to 99 polar
equations,
r1
through
r99
, if sufficient memory is available.
Equations are defined in terms of the independent variable
q
.
The default graph style is
»
(line) in
Pol
graphing mode.
¾
(shade above) and
¿
(shade below) graph styles are not
available in
Pol
graphing mode.
Setting the Graph Screen Window Variables
To display the polar window editor, select
WIND
from the
GRAPH
menu (
6
'
).
Pol
graphing mode has the same
window variables as
Func
graphing mode, except:
xRes
is not available in
Pol
graphing mode.
q
Min
,
q
Max
, and
q
Step
are available in
Pol
graphing mode.
The values shown in the picture to the right are the
defaults in
Radian
mode.
$
indicates that
yMin=
L
10
,
yMax=10
, and
yScl=1
are beyond the screen.
q
Min=0
Specifies the first
q
value to evaluate within the graph screen
q
Max=6.28318530718
Specifies the last
q
value to evaluate within the graph screen
q
Step=.13089969389957
Specifies the increment from one
q
value to the next
q
value
q
Max
default is 2
p
.
q
Step
default is
24.
Chapter 8: Polar Graphing
119
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Setting the Graph Format
To display the format screen in
Pol
graphing mode, select
FORMT
from the
GRAPH
menu
(
6
/
(
). Chapter 5 describes the format settings. Although the same settings are
available for
Func
,
Pol
, and
Param
graphing modes, the TI
-
86 retains in memory separate
format settings for each mode. In
Pol
graphing mode,
PolarGC
shows the cursor coordinates
in terms of
r
and
q
, the variables that define the equations.
Displaying the Graph
To plot the selected polar equations, you can select
GRAPH
,
TRACE
,
EVAL
,
RCGDB
, or a
ZOOM
,
MATH
,
DRAW
, or
RCPIC
operation, from the
GRAPH
menu. The TI
-
86 evaluates
r
for
each value of
q
(from
q
Min
to
q
Max
in intervals of
q
Step
) and then plots each point. As the
graph is plotted, the variables
q
,
r
,
x
, and
y
are updated.
Using Graph Tools in Pol Graphing Mode
The Free-Moving Cursor
The free-moving cursor in
Pol
graphing works the same as in
Func
graphing.
In
RectGC
format, moving the cursor updates the values of
x
and
y
; if
CoordOn
format is
selected,
x
and
y
are displayed.
In
PolarGC
format, moving the cursor updates
x
,
y
,
r
, and
q
; if
CoordOn
format is
selected,
r
and
q
are displayed.
DrawLine
graph format
typically displays a more
meaningful polar graph than
DrawDot
graph format.
120
Chapter 8: Polar Graphing
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Tracing a Polar Equation
To begin a trace, select
TRACE
from the
GRAPH
menu (press
6
)
). The trace cursor
appears on the first selected equation at
q
Min
.
In
RectGC
format, moving the trace cursor updates the values of
q
,
x
, and
y
; if
CoordOn
format is selected,
q
,
x
, and
y
are displayed.
In
PolarGC
format, moving the trace cursor updates
x
,
y
,
r
, and
q
; if
CoordOn
format is
selected,
r
and
q
are displayed.
To move the trace cursor... Press:
Along the graph of the equation by increments or decrements of
q
Step
"
or
!
From one equation to another
#
or
$
If you move the trace cursor beyond the top or bottom of the graph screen, the coordinate
values at the bottom of the screen continue to change appropriately.
If you have graphed a family of curves,
#
and
$
move through each curve before moving
to the next polar equation.
QuickZoom is available in
Pol
graphing; panning is not
(Chapter 6).
Chapter 8: Polar Graphing
121
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Moving the Trace Cursor to a
q
Value
To move the trace cursor to any valid
q
value on the current equation, enter the number.
When you enter the first digit, a
q
=
prompt is displayed in the bottom-left corner. The value
you enter must be valid for the current graph screen. When you have completed the entry,
press
b
to reactivate the trace cursor.
Using Zoom Operations
The
GRAPH
ZOOM
menu items, except
ZFIT
, work the same in
Pol
graphing as in
Func
graphing. In
Pol
graphing mode,
ZFIT
adjusts the graph screen in both the x and y directions.
The zoom operations affect only the
x
window variables (
xMin
,
xMax
, and
Xscl
) and the
y
window variables (
yMin
,
yMax
, and
yScl
), except
ZSTO
and
ZRCL
, which also affect the
q
window variables (
q
Min
,
q
Max
, and
q
Step
).
In the example,
r1=8sin(2.5
q
)
is graphed.
Values for
q
,
x
, and
y
are
displayed on the graph to the
right because
RectGC
graph
format is selected.
122
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The GRAPH MATH Menu
6
/
&
MATH DRAW FORMT STGDB RCGDB
DIST dy
à
dx dr
à
d
q
ARC TANLN
dr
à
d
q
Finds the numerical derivative (slope) of a function at a point
The distances calculated by
DIST
and
ARC
are distances in the rectangular coordinate plane.
dy
à
dx
and
dr
à
d
q
are independent of the
RectGC
or
PolarGC
format.
At a point where the derivative is undefined,
TANLN
will draw the line, but no result is
displayed or stored in
Ans
.
Evaluating an Equation for a Specified
q
When the trace cursor is not active, the
GRAPH
menu item
EVAL
evaluates selected polar
equations directly on the graph for a given value of
q
.
eval
in a program or from the home
screen returns a list of
r
values.
Drawing on a Polar Graph
The
GRAPH
DRAW
menu items work the same in
Pol
graphing as in
Func
graphing.
DRAW
instruction coordinates in
Pol
graphing mode are the x- and y-coordinates of the graph
screen.
DrInv
is not available in
Pol
graphing mode.
The other
GRAPH
MATH
menu items are the same as
described in Chapter 6.
09PARA.DOC TI-86, Chap 9, US English Bob Fedorisko Revised: 02/13/01 2:27 PM Printed: 02/13/01 3:02 PM Page 123 of 8
Preview: Parametric Graphing .........................................124
Defining a Parametric Graph ...........................................125
Using Graph Tools in Param Graphing Mode ..................128
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
9
Parametric
Graphing
124
Chapter 9: Parametric Graphing
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Preview: Parametric Graphing
Graph the parametric equation that describes the path of a ball kicked at an initial speed of
30 meters per second, at an initial angle of 25 degrees with the horizontal (from ground
level). How far does the ball travel? When does it hit the ground? How high does it go?
Select
Param
mode from the mode screen.
-
m
#
#
#
#
"
"
b
Display the equation editor and parametric
equation editor menu. Deselect all
equations and plots (if any are defined).
Define the path of the ball as
xt1
and
yt1
in
terms of
t
.
Horizontal: xt1=tv
0
cos(
q
)
Vertical: yt1=tv
0
sin(
q
)
N
1
à
2(gt
2
)
Gravity constant: g=9.8 m
à
sec
2
Define the vertical component vector as
xt2
and
yt2
and define the horizontal
component vector as
xt3
and
yt3
.
6
&
(
/
'
/
)
30
&
>
D
25
-
Œ
(
&
E
#
30
-
e
=
D
25
&
E
T
9
`
8
F
2
-
e
I
#
0
#
-
g
1
#
-
f
1
#
0
Change the graph style of
xt3àyt3
to
¼
(thick). Change the graph style of
xt2àyt2
and
xt1
/
yt1
to
À
(path).
.
/
)
$
$
)
)
$
$
$
)
)
In the example, ignore all
forces except gravity. For
initial velocity v
0
and angle
q
,
the position of the ball as a
function of time has
horizontal and vertical
components.
Chapter 9: Parametric Graphing
125
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Enter these window variable values.
tMin=0 xMin=
L
20 yMin=
L
5
tMax=5 xMax=100 yMax=15
tStep=.1 xScl=50 yScl=10
- f
0
#
5
#
`
1
# a
20
#
100
#
50
# a
5
#
15
#
10
Set
SimulG
and
AxesOff
graphing formats,
so the path of the ball and the vectors will
be plotted simultaneously on a clear graph
screen.
/ ( # # #
" b # # "
b
Plot the graph. The plotting action
simultaneously shows the ball in flight and
the vertical and horizontal component
vectors of the motion.
*
Trace the graph to obtain numerical results.
Tracing begins at
tMin
and traces the path
of the ball over time. The value displayed
for
x
is distance;
y
is height;
t
is time.
) "
Defining a Parametric Graph
The steps for defining a parametric graph are similar to the steps for defining a function
graph. This chapter assumes that you are familiar with Chapter 5: Function Graphing and
Chapter 6: Graph Tools. This chapter details those aspects of parametric graphing that
differ from function graphing.
To simulate the ball in flight,
change the graph style of
xt1
à
yt1
to
Á
(animate).
126
Chapter 9: Parametric Graphing
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Setting Parametric Graphing Mode
To display the mode screen, press
-
m
. To graph parametric equations, you must
select
Param
graphing mode before you enter equations, set the format, or edit window
variable values. The TI
-
86 retains in memory separate equation, format, and window data
for each graphing mode.
The GRAPH Menu
6
E(t)=
WIND ZOOM TRACE GRAPH
4
MATH DRAW FORMT STGDB RCGDB
4
EVAL STPIC RCPIC
parametric parametric parametric
equation window graph math
editor editor menu
Displaying the Parametric Equation Editor
To display the parametric equation editor, select
E(t)=
from the
GRAPH
menu in
Param
graphing
mode (
6
&
). The equation editor menu displayed on the bottom line is the same as the
Func
-mode equation editor menu, except that
t
and
xt
replace
x
and
y
, and
yt
displaces
INSf
.
In this editor, you can enter and display both the x and y
components of up to 99 parametric equations,
xt1
and
yt1
through
xt99
and
yt99
, if sufficient memory is available.
Each is defined in terms of the independent variable
t
.
Two components,
x
and
y
, define a single parametric
equation. You must define both
xt
and
yt
for each equation.
The default graph style is
»
(line) in
Param
mode.
¾
(shade above) and
¿
(shade below)
graph styles are not available in
Param
mode.
Chapter 5 describes these
GRAPH
menu items:
GRAPH
and
FORMT
.
Chapter 6 describes these
GRAPH
menu items:
ZOOM
,
TRACE
,
DRAW
,
STGDB
,
RCGDB
,
EVAL
,
STPIC
, and
RCPIC
.
A common application of
parametric graphs is
graphing equations over time.
Chapter 9: Parametric Graphing
127
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Selecting and Deselecting a Parametric Equation
When a parametric equation is selected, the equals signs (
=
) of both
xt
and
yt
are highlighted.
To change the selection status of a parametric equation, move the cursor onto either
xt
or
yt
, and then select
SELCT
from the equation editor menu. The status is changed for
xt
and
yt
.
Deleting a Parametric Equation
To delete a parametric equation using
DELf
, move the cursor to either
xt
or
yt
, and then
select
DELf
from the equation editor menu. Both components are deleted.
To delete a parametric equation using the
MEM
DELET
menu (Chapter 17), you must select
the
xt
component. If you select the
yt
component, the equation is retained in memory.
Setting the Graph Screen Window Variables
To display the parametric window editor, select
WIND
from
the
GRAPH
menu (
6
'
).
Param
graphing mode has the
same window variables as
Func
graphing mode, except:
xRes
is not available in
Param
mode.
tMin
,
tMax
, and
tStep
are available in
Param
mode.
The values shown in the picture to the right are the
defaults in
Radian
mode.
$
indicates that
yMin=
L
10
,
yMax=10
, and
yScl=1
are beyond the screen.
tMin=0
Specifies the starting
t
value
tMax=6.28318530718
Specifies the ending
t
value
tStep=.13089969389957
Specifies the increment from one
t
value to the next
tMax
default is 2
p
.
tStep
default is
24.
128
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Setting the Graph Format
To display the format screen in
Param
graphing mode, select
FORMT
from the
GRAPH
menu
(
6
/
(
). Chapter 5 describes the format settings. The TI
-
86 retains in memory
separate format settings for
Func
,
Pol
,
Param
, and
DifEq
graphing modes.
Displaying the Graph
To plot the selected parametric equations, you can select
GRAPH
,
TRACE
,
EVAL
,
RCGDB
, or
a
ZOOM
,
MATH
,
DRAW
, or
RCPIC
operation. The TI
-
86 evaluates
x
and
y
for each value of
t
(from
tMin
to
tMax
in intervals of
tStep
) and then plots each point defined by
x
and
y
. As the
graph is plotted, the variables
x
,
y
, and
t
are updated.
Using Graph Tools in Param Graphing Mode
The Free-Moving Cursor
The free-moving cursor in
Param
graphing works the same as in
Func
graphing.
In
RectGC
format, moving the cursor updates the values of
x
and
y
.; if
CoordOn
format is
selected,
x
and
y
are displayed.
In
PolarGC
format, moving the cursor updates
x
,
y
,
r
, and
q
; if
CoordOn
format is
selected,
r
and
q
are displayed.
Tracing a Parametric Function
To begin a trace, select
TRACE
from the
GRAPH
menu (
6
)
). When you begin a trace,
the trace cursor is on the first selected function at
tMin
.
In
RectGC
format, moving the trace cursor updates the values of
x
,
y
, and
t
; if
CoordOn
format is selected,
t
,
x
, and
y
and are displayed.
DrawLine
graph format
typically displays a more
meaningful parametric graph
than
DrawDot
graphing
format.
Chapter 9: Parametric Graphing
129
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In
PolarGC
format, moving the trace cursor updates
x
,
y
,
r
,
q
, and
t
; if
CoordOn
format is
selected,
r
,
q
, and
t
are displayed. The
x
and
y
(or
r
and
q
) values are calculated from
t
.
To move the trace cursor... Press:
Along the graph of the equation by increments or decrements of
tStep
"
or
!
From one equation to another
#
or
$
If you move the trace cursor beyond the top or bottom of the graph screen, the coordinate
values at the bottom of the screen continue to change appropriately. If you have graphed a
family of curves,
#
and
$
move through each curve before moving to the next parametric
function.
Moving the Trace Cursor to a t Value
To move the trace cursor to any valid
t
value on the current equation, enter the number.
When you enter the first digit, a
t=
prompt is displayed in the bottom-left corner. The value
you enter must be valid for the current graph screen. When you have completed the entry,
press
b
to reactivate the trace cursor.
Using Zoom Operations
The
GRAPH
ZOOM
menu items, except
ZFIT
, work the same in
Param
graphing as in
Func
graphing. In
Param
mode,
ZFIT
adjusts the graph screen in both the x and y directions.
QuickZoom is available in
Param
graphing; panning is
not (Chapter 6).
You can enter an expression
at the
t=
prompt.
In the example, the
parametric equation is:
xt1=95t cos 30
¡
yt1=95t sin 30
¡
N
16t
2
Also,
AxesOn
graph format is
set.
(The example on page 124 is
similar to this example.)
130
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The
GRAPH
ZOOM
menu items affect only the
x
window variables (
xMin
,
xMax
, and
xScl
) and
the
y
window variables (
yMin
,
yMax
, and
yScl
), except
ZSTO
and
ZRCL
, which also affect the
t
window variables (
tMin
,
tMax
, and
tStep
).
The GRAPH MATH Menu
6
/
&
MATH DRAW FORMT STGDB RCGDB
DIST dy
à
dx dy
à
dt dx
à
dt ARC
4
TANLN
dy
à
dx
Returns the derivative of
yt
divided by the derivative of
xt
dy
à
dt
Returns the derivative of the
yt
equation at a point with respect to
t
dx
à
dt
Returns the derivative of the
xt
equation at a point with respect to
t
The distances calculated by
DIST
and
ARC
are distances in the rectangular coordinate plane.
At a point where the derivative is undefined,
TANLN
will draw the line, but no result is
displayed or stored in
Ans
.
Evaluating an Equation for a Specified t
When the trace cursor is not active, the
GRAPH
menu item
EVAL
evaluates selected polar
equations directly on the graph for a given value of
t
.
eval
in a program or from the home
screen returns a list of x and y values in this form:
{
xt1(t)
yt1(t)
xt2(t)
xt2(t)
...
}
.
Drawing on a Parametric Graph
The
DRAW
menu items work in
Param
graphing the same as in
Func
graphing.
DRAW
instruction
coordinates in
Param
graphing are the
x
- and
y
-coordinate values of the graph screen.
The other
GRAPH
MATH
menu items are the same as
described in Chapter 5.
10DIFFEQ.DOC TI-86, Chap 10, US English Bob Fedorisko Revised: 02/13/01 2:28 PM Printed: 02/13/01 3:02 PM Page 131 of 20
Defining a Differential Equation Graph............................ 132
Entering and Solving Differential Equations ....................139
Using Graph Tools in DifEq Graphing Mode .................... 144
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
10
Differential
Equation Graphing
132
Chapter 10: Differential Equation Graphing
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Defining a Differential Equation Graph
Most steps for defining a differential equation graph are similar to the steps for defining a
function graph. This chapter assumes that you are familiar with Chapter 5: Function
Graphing and Chapter 6: Graph Tools. This chapter details aspects of differential equation
graphing that differ from function graphing.
Generally,
DifEq
graphing mode differs from other graphing modes in these ways.
You must select the field format or accept the default before defining the equations
(page 133).
If an equation is higher than first order, you must convert it to an equivalent system of
first-order differential equations, and then store the system in the equation editor
(page 140 and page 142).
When
FldOff
field format is selected, you must set initial conditions for each equation in
the system (page 136).
After you have selected the field format setting, you must select
AXES
from the
GRAPH
menu and enter axes information or accept the defaults (page 137).
Setting Differential Equation Graphing Mode
To display the mode screen, press
-
m
. To graph differential equations, you must
select
DifEq
graphing mode before you set the format, enter equations, or edit window
variable values. The TI
-
86 retains in memory separate format, equation, and window data
for each graphing mode.
Chapters 8 and 9 each begin
with an example; Chapter 10
has several differential
equation examples
throughout the chapter.
Chapter 10: Differential Equation Graphing
133
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The GRAPH Menu
6
Q'(t)= WIND INITC AXES GRAPH
4
FORMT DRAW ZOOM TRACE EXPLR
4
EVAL STGDB RCGDB STPIC RCPIC
equation initial conditions
editor editor explore with the free-moving cursor
differential equation axes differential equation
window editor editor format screen
Setting the Graph Format
To display the format screen in
DifEq
graphing mode,
select
FORMT
from the
GRAPH
menu (
6
/
&
).
The
RK Euler
and
SlpFld DirFld FldOff
format settings
are available only in
DifEq
mode.
The
RectGC PolarGC
,
DrawLine DrawDot
, and
SeqG SimulG
format settings are not available in
DifEq
graphing mode.
All other format settings are the same as described in Chapter 5.
Solution Method Format
RK
Uses the Runge-Kutta method to solve differential equations more accurately than the
Euler
solution method format, but not as fast
Euler
Uses the Euler method to solve differential equations; requires a number of iterations
between
tStep
values, so
EStep=
prompt replaces
difTol=
prompt on the window editor
Chapter 5 describes the
GRAPH
menu item
GRAPH
.
Chapter 6 describes these
GRAPH
menu items:
DRAW
,
ZOOM
,
TRACE
,
EVAL
,
STGDB
,
RCGDB
,
STPIC
, and
RCPIC
.
The TI
-
86 retains
independent format settings
for each graphing mode.
134
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Field Format
SlpFld
(slope field) Adds the slope field to the graph of only one first-order equation with
t
on
the x-axis and a specified
Qn
equation on the y-axis
DirFld
(direction field) Adds the direction field to the graph of only one second-order equation
with
Qx#
on the x-axis and
Qy#
on the y-axis
FldOff
(field off) Graphs all selected differential equations with
t
or
Q1
on the x-axis,
Q1
or
Q2
on the y-axis, and no field; initial conditions must be defined for all equations
(page 136)
The examples below show the basic slope and direction fields; all unspecified settings and
values are defaults. To replicate these examples, reset defaults, enter the specified
information in
DifEq
graphing mode, and then press
6
*
.
SlpFld
field format
DirFld
field format
Q'1=t
(y
'
=x)
Q'1=Q2
and
Q'2=
L
Q1
(y
"
=
L
y)
Displaying the Differential Equation Editor
To display the differential equation editor, select
Q'(t)=
from the
GRAPH
menu in
DifEq
graphing mode (
6
&
). The
DifEq
equation editor menu on the bottom line is the same
as the
Func
mode equation editor menu, except that
t
and
Q
replace
x
and
y
.
Axes information is stored to
GDB
and
PIC
variables.
To remove menus from a
graph, as shown in the
examples, press
:
.
Chapter 10: Differential Equation Graphing
135
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In this editor, you can enter and display a system of up to
nine first-order differential equations,
Q'1
through
Q'9
, if
sufficient memory is available. Equations are defined in
terms of the independent variable
t
and
à
or
Q'
.
You can refer to another differential equation variable in a
DifEq
equation, as in
Q'2=Q1
. However, you cannot enter a
list in a
DifEq
equation.
When the TI
-
86 calculates a differential equation system, it references all equations in the
equation editor, regardless of selection status, starting at
Q'1
. You must define
Q'
n
equation
variables consecutively, starting at
Q'1
. For example, if
Q'1
and
Q'2
are not defined, but you
attempt to solve an equation defined in
Q'3
, the calculator returns an error.
The TI
-
86 allows you to analyze each equation independently. For example, you can enter
Q'1=t
and
Q'2=t
2
and analyze each equation independently.
The TI
-
86 graphs only those selected equations that are appropriate for the specified axes.
The default graph style is
¼
(thick) in
DifEq
mode.
¾
(shade above),
¿
(shade below), and
Â
(dot) are not available in
DifEq
graphing mode.
Setting the Graph Screen Window Variables
To display the differential equation window editor, select
WIND
from the
GRAPH
menu (
6
'
).
DifEq
has the
same window variables as
Func
graphing mode, except:
xRes
is not available in
DifEq
mode.
tMin
,
tMax
,
tStep
, and
tPlot
are available in
DifEq
mode.
difTol
(
RK
) and
EStep
(
Euler
) are available in
DifEq
mode.
136
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The values shown in the picture on page 135 are defaults in
Radian
mode.
x
and
y
settings
correspond to the axes variables (page 137).
$
indicates that
xScl=1
,
yMin=
L
10
,
yMax=10
,
yScl=1
,
and
difTol=.001
(in
RK
format) or
EStep=1
(in
Euler
format) are beyond the screen.
tMin=0
Specifies the
t
value at which to begin evaluating within a graph screen
tMax=6.28318530718
Specifies the last
t
value to evaluate within a graph screen
tStep=.1308969389958
Specifies the increment from one
t
value to the next
t
value
tPlot=0
Specifies the point at which plotting begins (ignored when
t
is an axis)
difTol=.001
(in
RK
format) Specifies tolerance to help select step size for solving; must be
1
E
L
12
EStep=1
(in
Euler
format) Specifies Euler iterations between
tStep
values; must be an integer >0 and
25
Setting the Initial Conditions
To display the initial conditions editor, select
INITC
from
the
GRAPH
menu (
6
(
). On this editor, you can set
the initial value at
t=tMin
for each first-order equation in
the equation editor.
tMin
is the first
t
value to evaluate.
Q
[
1
is the initial value of
Q
n
. A small square next to an initial condition variable
indicates that a value is required for a defined differential equation.
You can enter an expression, list, or list name for initial conditions
tMin
and
Q
[
n
. When you
enter a list name, the elements are displayed when you press
b
,
#
or
$
.
If
SlpFld
or
DirFld
format is set, you need not specify initial conditions. The TI
-
86
returns the appropriate field with no specific solutions.
If
FldOff
format is set, you
must
specify initial conditions.
tMax
default is 2
p
.
tStep
default is
24.
Initial conditions information
is stored to
GDB
and
PIC
variables.
Chapter 10: Differential Equation Graphing
137
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Setting the Axes
To display the axes editor, select
AXES
from the
GRAPH
menu in
DifEq
mode (
6
)
).
x=
assigns a variable to the x-axis
y=
assigns a variable to the y-axis
dTime=
specifies a point in time (real number)
fldRes=
(resolution) sets number of rows (1 through 25)
At the
x=
and
y=
prompts, you can enter the independent variable
t
, as well as
Q
,
Q'
,
Q
n
, or
Q'
n
, where
n
is an integer
1 and
9. If you assign
t
to one axis and
Q
n
or
Q'
n
to the other
axis, only the equation stored to
Q
n
or
Q'
n
is plotted; other differential equations in the
equation editor are not plotted; their selection status is ignored.
dTime
is only valid for
second-order equations with
t
in either equation.
The axes editor and defaults for each field format are shown below. When
SlpFld
field
format is set, the x-axis is always
t
, so the
AXES: SlpFld
editor does not display
x=t
.
When
SlpFld
format is set: When
DirFld
format is set: When
FldOff
format is set:
Differential Equation Graphing Tips
Since the TI
-
86 plots slope fields and direction fields before it plots equations, you can
press
b
to pause the graph and view the fields with no solutions plotted.
If you do not specify initial conditions for the equations assigned to the axes, the TI
-
86
simply draws the field and stops. This gives you access to both the field format options
and the interactive initial conditions simultaneously.
Axes information is stored to
GDB
and
PIC
variables.
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The Built-In Variable fldPic
As the TI
-
86 plots a field, it stores the field and any displayed label, axes, or cursor
coordinate information to the built-in variable
fldPic
.
These actions do not update
fldPic
.
Switching the solving method format from
RK
to
Euler
or from
Euler
to
RK
Entering or editing any initial condition variable value (
Q
[
1
through
Q
[
9
)
Editing a value for
difTol
,
EStep
,
tMin
,
tMax
,
tStep
, or
tPlot
Changing a graph style
These actions update
fldPic
.
Editing an equation in the equation editor
Re-assigning an axis, editing a
dTime
value, or editing a
fldRes
value
Using a
GRAPH
ZOOM
menu item
Changing a format setting other than solving method format
Editing a value for
xMin
,
xMax
,
xScl
,
yMin
,
yMax
, or
yScl
Displaying the Graph
To plot the differential equations, you can select
GRAPH
,
TRACE
,
EVAL
, or
STGDB
, or a
DRAW
,
ZOOM
, or
STPIC
operation, from the
GRAPH
menu. The TI
-
86 solves each equation
from
tMin
to
tMax
. If
t
is not an axis, it plots each point beginning at
tPlot
; otherwise, it
begins at
tMin
. As a graph is plotted, the variables
x
,
y
,
t
, and
Q
n
are updated.
tStep
affects trace resolution and graph appearance, but not the accuracy of the trace
values.
tStep
does not determine the step size for solving; using the
RK
algorithm (Runge-
Kutta 2-3) determines the step size. If the x-axis is
t
, setting
tStep
<(
tMax
N
tMin
)
à
126
increases plotting time without increasing accuracy.
Stat plot and screen drawing
s
are not stored to
fldPic
.
Chapter 10: Differential Equation Graphing
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Entering and Solving Differential Equations
In
Func
graphing mode,
x
is the independent variable and
y
is the equation variable. To avoid
conflict between
Func
equations and
DifEq
equations on the TI
-
86,
t
is the independent
variable and
Q'
n
is the equation variable in
DifEq
graphing mode. Therefore, when you enter
an equation in the differential equation editor, you must express it in terms of
t
and
Q'
n
.
For example, to express the first-order differential equation y'=x
2
, you would substitute
t
2
for x
2
and
Q'1
for y', and then enter
Q'1=t
2
in the equation editor.
Graphing in SlpFld Format
Display the mode screen and set
DifEq
graphing mode.
-
m
#
#
#
#
"
"
"
b
Display the format screen and set
SlpFld
field format.
6
/
&
#
#
#
#
#
b
Display the equation editor and store the
differential equation y'=x
2
, substituting
Q'1
for y' and
t
for x. Clear any other
equations.
&
&
I
Display the initial conditions editor and
enter the initial conditions. A small square
indicates that an initial condition is required.
-
g
3
In the example, the default
window variable values are
set initially.
140
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Display the axes editor and enter the
equation variable for which you want to
solve. (Do not set
y=Q
.)
Accept or change
fldRes
(resolution).
) &
1
Display the graph. With the default
window variable values set, the slope
fields for this graph are not very
illustrative.
- i
Change the window variables
xMin
,
xMax
,
yMin
, and
yMax
.
Select
TRACE
from the
GRAPH
menu to re-
plot the graph and activate the trace cursor.
Trace the solution. The trace cursor
coordinates for
t
and
Q1
are displayed.
' # # # #
0
#
5
# #
0
#
20
/ )
" and !
Transforming an Equation into a First-Order System
On the TI
-
86, to enter a second-order or higher (up to ninth-order) differential equation, you
must transform it to a system of first-order differential equations. For example, to enter the
second-order differential equation y''=
L
y, you must transform it to two first-order
differential equations, as shown in the chart below.
Differentiate... Define the variables as... And then substitute:
Q'1
=y'
Q1
=y
Q'1=Q2
(since
Q'1
=y'=
Q2
)
Q'2
=y''
Q2
=y'
Q'2=
L
Q1
In
SlpFld
field format,
x=t
is
always true;
y=Q1
and
fldRes=15
are the default
axes settings.
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Graphing in DirFld Format
Display the mode screen and set
DifEq
graphing mode.
- m # # #
# " " " b
Display the format screen and set
DirFld
graphing format.
6 / & #
# # # # " b
Display the equation editor and store the
transformed system of differential
equations for y''=
L
y to the equation editor,
substituting
Q1
for y and
Q2
for y'.
& '
2
# a '
1
Display the initial conditions editor and enter
the initial conditions if you want a specific
solution. To enter a list of initial conditions,
use
{
and
}
from the
LIST
menu.
- g -
&
1
P
2
P
5
'
# & -~ P
4
P
5
`
75
'
Display the axes editor and enter the two
equation variables for which you want to
solve. You must omit the prime mark (
'
).
Accept or change
fldRes
(resolution).
- h &
1
#
&
2
Select
ZSTD
from the
GRAPH
ZOOM
menu
to set the standard window variable values
and display the graph.
Clear the
GRAPH
menu from the screen.
. / ( )
:
In
DifEq
graphing mode,
t
is
the independent variable and
Q'
n
is the dependent variable,
where
n
1 and
9.
In the example, the default
window variable values are
set initially.
When
DirFld
field format is
selected,
x=Q1
,
y=Q2
,
dTime=0
, and
fldRes=15
are
the default axes settings.
Since
t
is not part of the
equation,
dTime
is ignored.
142
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Graphing a System of Equations in FldOff Format
For this example, you must transform the fourth-order differential equation
y
(4)
N
y=e
L
x
into an
equivalent system of first-order differential equations, as shown in the chart below.
Differentiate... Define the variables as... And then substitute:
t
=x
Q'1
=y'
Q1
=y
Q'1
=
Q2
(since
Q'1
=y'=
Q2
)
Q'2
=y''
Q2
=y'
Q'2
=
Q3
Q'3
=y'''
Q3
=y''
Q'3
=
Q4
Q'4
=y
(4)
Q4
=y'''
Q'4
=e
L
t
+
Q1
(since
Q'4
=y
(4)
=e
L
x
+y=e
L
t
+
Q1
)
Display the mode screen and set
DifEq
graphing mode.
-
m
#
#
#
#
"
"
"
b
Display the format screen and set
FldOff
field format.
6
/
&
#
#
#
#
#
"
"
b
Display the equation editor and store the
transformed system of differential
equations for y
(4)
=e
L
x
+y, substituting as
shown in the chart.
Deselect
Q'3
,
Q'2
, and
Q'1
to plot
Q'4=e^(
L
t)+Q1
only.
&
'
2
#
'
3
#
'
4
#
-
D
a
&
E
\
'
1
$
*
$
*
$
*
In
DifEq
graphing mode,
t
is
the independent variable and
Q'
n
is the equation variable,
where
n
1 and
9.
Chapter 10: Differential Equation Graphing
143
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Display the window editor and set the
window variable values.
- f #
10
#
`
01
# #
0
#
# # a
4
#
4
Display the initial conditions editor and enter
the initial conditions. A small square
indicates that an initial condition is required.
(
3
# a
5
`
25
#
7
`
5
#
a
5
`
75
Display the axes editor. Enter the equation
variables for which you want to solve.
)
Display the graph. Explore the equation
with the trace cursor.
Enter a
t
value to move the trace cursor to
the solution for that
t
value. The
t
and
Q4
coordinates are displayed.
. / )
" and !
4
b
When
FldOff
field format is
selected,
x=t
and
y=Q
are the
default axes settings.
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Solving a Differential Equation for a Specified Value
On the home screen in
DifEq
graphing mode, you can solve a
differential equation stored to a specified independent variable
value or expression. The syntax is:
Q'
n
(
value
)
.
The equation must be stored to a
DifEq
equation variable
(
Q'1
through
Q'9
).
The initial conditions must be defined.
The result sometimes varies, depending on the axes settings.
Using Graph Tools in DifEq Graphing Mode
The Free-Moving Cursor
The free-moving cursor works in
DifEq
mode as it does in
Func
graphing. The cursor
coordinate values for
x
and
y
are displayed, and the variables are updated.
Tracing a Differential Equation
To begin a trace, select
TRACE
from the
GRAPH
menu (
6
/
)
). The trace cursor
appears on the first equation at or near
tPlot
(or
tMin
, if
t
is an axis).
The trace coordinates displayed at the bottom of the screen reflect the axes settings. For
example, if
x=t
and
y=Q1
, then
t
and
Q1
are displayed. If
t
is not an axis, three trace values
are displayed. If
t
is an axis, only
t
and the variable designated as the y-axis are displayed.
The trace cursor moves in increments or decrements of
tStep
. As you trace an equation, the
coordinates are updated and displayed. If the cursor moves off the screen, the coordinate
values displayed at the bottom of the screen continue to change appropriately.
To paste
'
to the home
screen, you can select it from
the
CHAR
MISC
menu or fro
m
the
CATALOG
.
Due to TI
-
86 system
requirements, you must
express
Q1(3)
as
Q'1(3)
on
the calculator.
QuickZoom is available in
DifEq
graphing; panning is
not (Chapter 6).
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Moving the Trace Cursor to a t Value
To move the trace cursor to any valid
t
value on the current equation, enter the number.
When you enter the first digit, a
t=
prompt is displayed in the bottom-left corner. The value
you enter must be valid for the current graph screen. When you have completed the entry,
press
b
to reactivate the trace cursor.
Drawing on a Differential Equation Graph
The
GRAPH
DRAW
menu items work the same in
DifEq
graphing mode as in
Func
graphing.
DRAW
instruction coordinates are the x- and y-coordinates of the graph screen.
DrEqu
is available only in
DifEq
mode.
DrInv
is not available in
DifEq
graphing mode.
Drawing an Equation and Storing Solutions to Lists
To draw a solution on the current graph screen and store the results to specified list names,
the syntax is:
DrEqu(
xAxisVariable
,
yAxisVariable
ã
,
xList
,
yList
,
tList
ä
)
xAxisVariable
and
yAxisVariable
specify the axes on which the drawing is based; they may
differ from the current graph screen’s axes settings.
Values for
t
and
Q
are
displayed on the graph to the
right because
x=t
and
y=Q
graph axes are selected.
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xList
,
yList
, and
tList
are optional list names to which you can store the solutions
x
,
y
, and
t
. You then can display the lists on the home screen or in the list editor (Chapter 11).
Use the free-moving cursor to select initial conditions.
You cannot trace the drawing. However, you can plot
xList
,
yList
, or
tList
as a stat plot
after you draw the equation, and then trace them (Chapter 14). Also, you can fit statistical
regression models to the lists (Chapter 14).
Display the mode screen and set
DifEq
graphing mode.
-
m
#
#
#
#
"
"
"
b
Display the format screen and set
DirFld
field format.
6
/
&
#
#
#
#
#
"
b
Display the equation editor and store the
equations
Q'1=Q2
and
Q'2=
L
Q1
. (Delete
all other equations.)
&
'
2
#
a
'
1
Remove the format screen, and then select
DrEqu
from the
GRAPH
DRAW
menu.
DrEqu(
is pasted to the home screen.
.
.
6
/
'
&
Assign variables to the x- and y-axes.
Specify list names to which to store the
solution lists for
x
,
y
, and
t
.
1
ã
Q
ä
1
P
1
ã
Q
ä
2
P
1
ã
L
ä
1
ã
X
ä
P
1
ã
L
ä
1
ã
Y
ä
P
1
ã
L
ä
1
ã
T
ä
E
DrEqu(
does not store values
to
x
,
y
, or
t
.
In the example, the default
window variable values are
set. If necessary, select
ZSTD
from the
GRAPH
ZOOM
menu.
If you select
FldOff
field
format, you must enter initial
conditions before you use
DrEqu(
.
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Display the graph screen and plot the
direction field.
Move the free-moving cursor to the initial
condition coordinates you want.
b
" # ! $
Draw the solution. The solution lists for
x
,
y
, and
t
are stored to
LX
,
LY
, and
LT
.
The
Again?
prompt is displayed and
ALPHA-lock is on for
ã
Y
ä
and
ã
N
ä
only.
To use
DrEqu(
again with new initial
conditions, press
ã
Y
ä
, ", #, !, or $.
b
To leave
DrEqu(
and display the
GRAPH
menu, press
ã
N
ä
or ..
Using ZOOM Operations
The
GRAPH
ZOOM
menu items, except
ZFIT
, work the same in
DifEq
graphing mode as in
Func
graphing mode. In
DifEq
graphing mode,
ZFIT
adjusts the graph screen in both the x
direction and y direction.
The
ZOOM
menu items affect only the
x
(
xMin
,
xMax
, and
xScl
) and
y
(
yMin
,
yMax
, and
yScl
)
window variables. The
t
window variables (
tMin
,
tMax
,
tStep
, and
tPlot
) are not affected,
except with
ZSTD
and
ZRCL
. You may want to edit the
t
window variables to ensure that
sufficient points are plotted.
ZSTD
sets
difTol=.001
and
t
and
Q
as the axes.
In the example, since no
initial conditions were set, the
equation in
Q'1
is not plotted.
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Drawing Solutions Interactively with EXPLR
Display the mode screen and set
DifEq
graphing mode.
- m # # #
# " " " b
Display the format screen and set
FldOff
field format.
6 / & #
# # # # " "
b
Display the equation editor and store the
equation
Q'1=.001Q1(100
N
Q1)
. (Delete all
other equations.)
& `
001
'
1
D
100
T '
1
E
Set the axes to
x=t
and
y=Q1
. - h # "
1
Display the window editor and set the
window variable values.
- f #
100
#
`
2
# # #
100
# # #
110
Display the initial conditions editor and
enter the initial condition.
(
10
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Select
EXPLR
from the
GRAPH
menu.
Move the free-moving cursor to the initial
condition for which you want to solve.
/ *
" # ! $
Draw the solution to
Q1
, using the cursor
coordinates (x,y) as initial condition
(
t
,
Q'1(t)
).
b
To continue drawing more solutions, move the free-moving cursor and then press
b
.
To stop using
EXPLR
, press
.
.
If
SlpFld
or
DirFld
is set, the axes are set to specific solutions automatically.
For
SlpFld
,
x=t
and
y=Q1
are set.
For
DirFld
,
x=Q1
and
y=Q2
are set.
If the axes are set to a specific solution
t
,
Q
n
, or
Q'
n
, that solution is drawn.
If the axes are not set to a specific solution and
t
is one variable and
Q
is the other,
Q1
is drawn.
If both axes are set to a
Q
variable, executing
EXPLR
results in an error.
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Evaluating Differential Equations for a Specified t
When the trace cursor is not active, the
GRAPH
menu item
EVAL
evaluates currently selected
differential equations
Q
n
for a specified value of
t
,
tMin
t
tMax
. You can use it directly on
the graph. In a program or from the home screen,
eval
returns a list of
Q
values.
When
DirFld
or
SlpFld
field format is set, you must specify initial conditions before using
EVAL
.
11LISTS.DOC TI-86, Chap 11, US English Bob Fedorisko Revised: 02/13/01 2:30 PM Printed: 02/13/01 3:03 PM Page 151 of 16
Lists on the TI
-
86.............................................................152
Creating, Storing, and Displaying Lists ............................153
The List Editor..................................................................156
Using List Operations....................................................... 159
Using Mathematical Functions with Lists ........................ 161
Attaching a Formula to a List Name ................................ 162
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
11
Lists
152
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Lists on the TI-86
A list is a set of real or complex elements, as in
{5,
L
20,13,9}
. On the TI
-
86, you can:
Enter a list directly in an expression (page 153)
Enter a list and store it to a list name (variable) (page 154)
Enter a list name in the list editor (page 156), and then enter elements directly or use an
attached formula to generate them automatically (page 161)
Collect data with the Calculator-Based Laboratory™ (CBL 2™/CBL™) or Calculator-Based
Ranger™ (CBR) and store it to a list name on the TI
-
86 (Chapter 18)
Create lists dynamically using the
LIST
OPS
menu item
seq
(page 159)
On the TI
-
86, you can use a list:
As a set of values for an argument in a function to return a list of answers (Chapter 1)
As part of an equation to graph a family of curves (Chapter 5)
As a set of statistical data to analyze with statistical functions and plot on the graph
screen (Chapter 14)
The LIST Menu
-
{ } NAMES EDIT OPS
open brace list names list operations
menu menu
close brace list editor
When you enter a list,
{
(open brace) specifies the beginning and
}
(close brace) specifies
the end. To paste
{
or
}
to the cursor location, select either from the
LIST
menu.
The length and number of
lists you can store in the
TI
-
86 is limited only by
memory capacity.
If you enter more than one
list in an equation or
expression, all lists must
have the same number of
elements.
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The LIST NAMES Menu
-
(
{ } NAMES EDIT OPS
fStat xStat yStat
Each user-created list name is added to the
LIST
NAMES
menu and
VARS LIST
screen. List
names, including
fStat
,
xStat
, and
yStat
, are sorted in alphanumeric order in both places.
Creating, Storing, and Displaying Lists
Entering a List Directly in an Expression
To enter a list directly, the syntax is:
{
element1
,
element2
,
...
,
element n
}
Enter any part of the expression that precedes
the list.
Select
{
from the
LIST
menu to begin the list.
5
M
-
&
Enter each list element, separating each from
the other with a comma. Each list element can
be an expression.
Select
}
from the
LIST
menu to end the list.
a
16
P
4
P
4
I
P
3
-
~
'
Enter any part of the expression that follows
the list.
Evaluate the expression. Any elements that are
expressions are evaluated first.
F
4
b
The
LIST
NAMES
menu
shown here has no user-
created list names.
Chapter 14 describes
fStat
,
xStat
, and
yStat
.
An ellipsis (...) indicates that
a list continues beyond the
screen. Use
"
and
!
to
scroll the list.
154
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Creating a List Name by Storing a List
To store a list, the syntax is:
{
element1
,
element2
,
...
,
element n
}
listName
Enter a list directly. (To store a result expressed as
a list and currently stored in
Ans
, as shown in the
example, begin these steps at step 2.)
Paste
to the cursor location. ALPHA-lock is on.
(steps 2
through 5
above)
X
Enter the list name. Either select a name from the
LIST
NAMES
menu or directly enter a name one to
eight characters long, starting with a letter.
Store the list to the list name.
ã
A
ä
ã
B
ä
ã
C
ä
1
1
2
3
b
Displaying List Elements Stored to a List Name
Enter the list name on the home screen;
either select it from the
LIST
NAMES
menu
or enter the characters.
Display the list elements.
-
(
&
b
You need not enter the close
brace
(
}
)
when you use
X
to store a list name.
To delete a list name from
memory, use the
MEM
DELETE:LIST
screen
(Chapter 17).
The TI
-
86 distinguishes
between uppercase and
lowercase letters in list
names. For example,
ABC123
,
Abc123
, and
abc123
are three different list names.
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Displaying or Using a Single List Element
To display or use a single list element, the syntax is:
listName
(
element#
)
Enter the list name; either select it from the
LIST
NAMES
menu or enter the characters.
In parentheses, enter the element’s place
number in the list.
Display the list element.
-
(
&
D
4
E
b
Storing a New Value to a List Element
To store a value to a current element or one element beyond the end of a list, the syntax is:
value
listName
(
element#
)
Enter the value to be stored in a current list
element or one element beyond the end.
Paste
to the cursor location.
-
ˆ
18
X
Enter the list name; either select it from the
LIST
NAMES
menu or enter the characters.
&
Enter the element’s place number in
parentheses. (In the example,
5
is one
beyond the current dimension of
ABC123
).
Enter the new value to the element number.
(
18
is evaluated and added as the fifth
element.)
1
D
5
E
b
listName
(
element#
)
is valid
as part of an expression.
element
# is
1 and
the
dimension of the list.
value
can be an expression.
156
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Complex List Elements
A complex number can be a list element. If at least one list
element is a complex number, all elements in the list are
displayed as complex. (
L
4 results in a complex number.)
The List Editor
-
)
The list editor is a table where you can store, edit, and view up to 20 lists that are in
memory. Also, you can create list names and attach formulas to lists in the list editor.
List names
Table of elements
Entry line with current column
list name and element number
Current column number
List editor menu
The List Editor Menu
-
)
{ } NAMES
"
OPS
44
REAL
"
Designates the beginning and end of a formula to be attached to a list name
4
REAL
Converts the current list to a list of real numbers
To use
LIST
OPS
menu items (or any other functions or instructions) in the list editor, the
cursor location must be appropriate for the result. For example, you can use the
LIST
OPS
menu item
sortA
when a list name is highlighted but not when an element is highlighted.
You also can press
-
š
'
to display the list editor.
The list editor abbreviates list
names and element values
when necessary. The entry
line displays entire list names
and element values.
The list editor menu items
{
,
}
,
NAMES
, and
OPS
are
identical to the
LIST
menu
items (page 152).
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Creating a List Name in the Unnamed Column
Display the list editor.
Move the cursor to the unnamed column
(column 4). The
Name=
prompt is displayed
in the entry line. ALPHA-lock is on.
- )
$ " " "
Enter the list name. The list name is displayed
at the top of the current column. In the entry
line, a list name prompt is displayed. The
name becomes a
LIST
NAMES
menu item and
a
VARS
LIST
screen item.
ã
X
ä
ã
Y
ä
ã
Z
ä
b
Inserting a List Name into the List Editor
Move the cursor to column
3
.
Insert a new, unnamed column. List names shift
right, clearing column
3
. The
Name=
prompt and
LIST
NAMES
menu are displayed.
!
- p
Select
ABC12
from the
LIST
NAMES
menu to
insert the list name
ABC123
into column
3
.
Elements stored to
ABC123
fill the column
3
table of elements. The full value of all
ABC123
elements is displayed in the entry line.
& b
After memory is reset,
xStat
,
yStat
, and
fStat
are stored to
columns
1
,
2
, and
3
.
Resetting defaults does not
affect the list editor.
To move from the list name i
n
column 1 to the unnamed
column, press
!
"
.
If all 20 columns have list
names, you must remove a
list name to make room for
the unnamed column.
To cancel the list name
insertion, press
:
.
If a formula were attached to
ABC123
, the formula would
be displayed in the entry line
instead of the list shown in
step 3 (page 162.)
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Displaying and Editing a List Element
Move the cursor onto the fifth element of
ABC123
. In the entry line, the list name,
the element number in parentheses, and
the element’s full value are displayed.
# # # # #
Switch to edit-element context and edit the
element in the entry line.
5
M D
6
- ~ E
F
4
Enter the edited element. Any expression
is evaluated and the value is stored to the
current element.
b (or # or $)
Deleting Elements from a List
To delete a single element from a list, move the cursor onto the element and press
3
. The
element is deleted. You can clear all elements from a list in any of three ways.
In the list editor, press
$
to move the cursor onto a list name and press
:
b
.
In the list editor, move the cursor onto each element, and then press
3
one by one.
On the home screen or in the program editor, enter
0dimL
listName
to set the
dimension of
listName
to
0
(A to Z Reference).
Removing a List from the List Editor
To remove a list from the list editor, move the cursor onto the list name and then press
3
.
The list is not deleted from memory; it is only removed from the list editor.
To cancel any editing and
restore the original element
at the cursor, press
:
b
.
You can enter an expression
as an element.
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You can remove all user-created lists from the list editor and restore list names
xStat
,
yStat
,
and
fStat
to columns
1
,
2
, and
3
in either of two ways.
Use
SetLEdit
with no arguments (page 161).
Reset all memory (Chapter 17). Resetting defaults does not affect the list editor.
Using List Operations
The LIST OPS (Operations) Menu
-
*
{ } NAMES EDIT OPS
dimL sortA sortD min max
4
sum prod seq li
4
vc vc
4
li
4
Fill aug cSum Deltal Sortx
4
Sorty Select SetLE Form
dimL list
Returns the dimension of (or number of elements in)
list
#ofElements
dimL
listName
Creates
listName
as a list that is
#ofElements
in length; each
element is a
0
#ofElements
dimL
listName
Redimensions an existing
listName
; previously entered elements
within the new dimension remain; each new list element is a
0
; each
element in the old list that is outside the new dimension is deleted
sortA list
Sorts
list
elements in ascending order, from low to high values
sortD list
Sorts
list
elements in descending order, from high to low values
For all
LIST
OPS
menu items
except
Fill(
and sometimes
dimL
, a directly entered list
(
{
element1
,
element2
,
...
}
)
is
valid for the
list
argument.
SortA
and
SortD
sort
complex lists based on
magnitude (modulus).
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min(list)
Returns the smallest element of a real or complex
list
max(list)
Returns the largest element of a real or complex
list
sum list
Returns the sum of all the elements of a real or complex
list
,
adding from the last element to the first
prod list
Returns the product of all the elements of a real or complex
list
seq(expression,variable,
begin
,endã,stepä)
Returns a list in which each element is the result of the evaluation
of
expression
with regard to
variable
for the values ranging from
begin
to
end
in intervals of
step
(
step
can be negative)
li
4
vc
list
li
4
vc {element1,element2,
...
}
Converts a real or complex
list
to a vector
vc
4
li
vector
vc
4
li
ã
element1,element2,
...
ä
Converts a real or complex
vector
to a list
Fill(number,listName)
Stores a real or complex
number
to every element of
listName
aug(listA,listB)
(augment) Concatenates the real or complex elements of
listA
and
listB
cSum(list)
Returns a list of the cumulative sums of real or complex
list
elements, starting with the first element and proceeding to the last
Deltalst(list)
Returns a list containing the differences between consecutive
elements for all elements in a real or complex
list
Sortx ãListName,ListName,
frequencyListNameä
In ascending order of
x
elements, sorts
xListName
, sorts
x
and
y
data pairs, and optionally, their frequencies, in
xListName
,
yListName
, and
frequencyListName
;
xStat
and
yStat
are defaults
Sorty ãxListName,ListName,
frequencyListNameä
In ascending order of
y
elements, sorts
xListName
, sorts
x
and
y
data pairs, and optionally, their frequencies, in
xListName
,
yListName
, and
frequencyListName
;
xStat
and
yStat
are defaults
For a complex list,
min
or
max
returns the smallest or
largest magnitude (modulus).
Selecting
Deltal
from the
menu pastes
Deltalst(
to the
cursor location.
For
Sortx
and
Sorty
, both
lists must have the same
number of elements.
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Select(xListName
,
yListName
)
Selects one or more specific data points from a scatter plot or
xyLine plot (only), then stores the selected data points to
x
ListName
and
yListName
(Chapter 14)
SetLEdit
ãcolumn1ListName
,
column2ListName,
...
,
column20ListNameä
Sets up the list editor;
SetLEdit
with one to 20
ListNames
loads
them in the specified order;
SetLEdit
with no arguments removes
all current list names from the list editor and enters the default
lists
xStat
,
yStat
, and
fStat
to columns 1, 2, and 3
Form("formula",listName)
Attaches
formula
to
listName
;
formula
resolves to a list, which is
dynamically stored and updated in
listName
(page 162)
Using Mathematical Functions with Lists
You can use a list as a single argument for many TI
-
86 functions; the result is a list. The
function must be valid for every element in the list; however, when graphing, undefined
points do not result in an error.
When you use lists for two or more arguments in the same function, all lists must have the same
number of elements (equal dimension). Here are some examples of a list as a single argument.
{1,2,3}+10
returns
{11 12 13}
{4,16,36,64}
returns
{2 4 6 8}
{5,10,15}¹{2,4,6}
returns
{10 40 90} sin {7,5}
returns
{.656986598719
L
.958924274663}
3+{1,7,(2,1)}
returns
{(4,0) (10,0) (5,1)} {1,15,36}<19
returns
{1 1 0}
Selecting
SetLE
from the
menu pastes
SetLEdit
to the
cursor location.
You can create new list
names as
SetLEdit
arguments.
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Attaching a Formula to a List Name
You can attach a formula to a list name so that the formula generates a list that is stored
and dynamically updated in the list name.
When you edit an element of a list that is referenced in the formula, the corresponding
element in the list to which the formula is attached is updated.
When you edit the formula itself, all elements in the list to which the formula is
attached are updated.
To attach a formula to a list name on the home screen or in the program editor, the syntax is:
Form("
formula
",
listName
)
When you enter a new list name as the second argument for
Form(
, the list name is created
and stored in the
LIST
NAMES
menu and
VARS LIST
screen upon execution.
Store elements to a list name.
Select
Form
from the
LIST
OPS
menu;
Form(
is pasted to the cursor location.
-
&
1
P
2
P
3
'
X
ã
L
ä
1
1
b
*
/
/
/
)
Enter a formula in quotation marks.
Enter a comma and then the list name to
which you want to attach the formula.
Attach the formula to the list name.
-
&
1
ã
L
ä
1
\
10
&
P
1
1
ã
A
ä
ã
D
ä
ã
D
ä
1
10
E
b
You cannot edit an element
of a list created from an
attached formula unless you
first detach the formula from
the list name.
When you include more than
one list name in an attached
formula, each list must have
the same dimension.
Begin these steps on a blank
line on the home screen.
To view a formula attached to
a list name, use the list editor
(page 157).
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Comparing an Attached List with a Regular List
To see the differences between an attached list and a regular list, follow these steps. The
example below builds on the example above for attaching a formula to a list. Notice that the
formula in step 1 below is not attached to
LX
because it is not set off by quotation marks.
Generate a regular list by storing the
expression
L1+10
to the list name
LX
.
1
ã
L
ä
1
\
10
X
ã
L
ä
ã
X
ä
b
Change the second element in
L1
to
L
8
and
display the edited list.
a
8
X
ã
L
ä
1
1
D
2
E
-
1
ã
L
ä
1
b
Compare the elements of the regular list
LX
with
ADD10
, to which the formula
L1+10
is
attached. Notice that element 2 of
LX
is
unchanged. Meanwhile, element 2 of
ADD10
has been recalculated, since element 2 of
L1
has been edited.
-
(
'
b
)
b
Using the List Editor to Attach a Formula
Display the list editor.
Highlight the list name to which you want to
attach the formula.
Enter the formula in quotation marks.
-
)
$
"
)
4
M
(
'
-
)
If other list names are stored
on the
LIST NAMES
menu,
pressing
&
and
(
may not
paste
ADD10
and
LX
to the
home screen as shown.
In the example, only fStat,
xStat
, and
yStat
are on the
LIST NAMES
menu and
xStat={
L
2,9,6,1,
L
7}
.
The attached formula must
be set off by quotation marks.
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Attach the formula and generate the list.
The TI
-
86 calculates each list element.
A lock symbol is displayed next to the list
name to which the formula is attached.
b
To edit an attached formula, press
b
in step 3, and then edit the formula.
Using the List Editor With Attached-Formula Lists
When you edit an element of a list
referenced in an attached formula,
the TI
-
86 updates the corresponding
element in the list to which the
formula is attached.
When you edit or enter elements of a displayed list in any of the three current list editor
columns while an attached-formula list also is displayed, the TI
-
86 takes slightly longer to
execute the edit or entry. To reduce this effect, move lists with formulas off the current three-
column display, either by scrolling columns to the left or right or by rearranging the list editor.
Executing and Displaying Attached Formulas
An attached formula must resolve to a list upon execution. Some examples of formulas that
resolve to a list are
"5¹xStat"
,
"seq(x,x,1,10)"
, and
"{3,5,
L
8,4}
2
à
10"
. Execution of the formula
occurs when you attempt to display the list to which the formula is attached. Also, the
formula is executed whenever a list referenced by the formula is modified — whether on
the home screen, in the list editor, or in a program.
The list editor displays a
formula-lock symbol next to
each list name that has a
formula attached to it.
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You can successfully attach to a list a formula that does not yet resolve to a list. For
example, you can attach
"5¹xStat"
to the list name
BY5
with no elements stored to
xStat
.
However, if you attempt to display
BY5
when
xStat
has no elements, an error occurs.
When you attach such a formula to a list name in the list editor, the formula is successfully
attached, but an error occurs. This is because the list editor attempts to execute the
formula immediately after attaching it to the list name.
To view the list editor again, you must return to the home screen and either enter
something to cause the formula to resolve to a list or remove the attached-formula list from
the list editor using the
LIST
OPS
menu item
SetLE
(page 161).
Handling Errors Related to Attached Formulas
On the home screen, you can attach to a list a formula that references another list that has
no elements (dimension is
0
; page 161). However, you cannot display the attached-formula
list in the list editor or on the home screen until you enter at least one element to the list
that the formula references.
Tip:
If an error menu is returned when you attempt to display an attached-formula list in
the list editor, you can select
GOTO
, write down the formula that is attached to the list
name, and then press
:
b
to detach (clear) the formula. Then you can use the list
editor to find the source of the error. After making the appropriate changes, you can re-
attach the formula to the list name.
If you do not want to clear the formula, you can select
QUIT
, display the referenced list on
the home screen, and find and edit the source of the error. To edit an element of a list on
the home screen, store the new value to
listName
(
element#
)
(page 155).
All elements of a list
referenced by an attached
formula must be valid for the
attached formula.
166
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Detaching a Formula from a List Name
You can detach a formula in any of five ways.
Use
dimL
to change the dimension of the list (page 159).
Use
value
listName
(
element#
)
to store
value
to an attached-formula list element.
Use
""
listName
, where
listName
is the attached-formula list.
In the list editor, move the cursor onto the name of the attached-formula list, and then
press
b
:
b
. All list elements remain, but the formula is detached and the
lock symbol disappears.
In the list editor, move the cursor onto an element of the attached-formula list. Press
b
, edit the element, and then press
b
. The element changes, the formula is
detached, and the lock symbol disappears. All other list elements remain.
Editing an Element of a Attached-Formula List
As described above, one way to detach a formula from a list name is to edit an element of
the attached-formula list. The TI
-
86 protects against inadvertently detaching the formula
from the list name when you move the cursor onto one of the elements.
Because of the protection feature, you must press
b
before you can edit an element of
an attached-formula list. The protection feature prevents you from deleting an element of an
attached-formula list. To delete an element of a attached-formula list, you must first detach
the formula in any of the ways described above.
12VECTR.DOC TI-86, Chap 12, US English Bob Fedorisko Revised: 02/13/01 2:31 PM Printed: 02/13/01 3:03 PM Page 167 of 10
Vectors on the TI
-
86 ........................................................ 168
Creating, Storing, and Displaying Vectors........................ 169
Using Mathematical Functions with Vectors.................... 176
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Vectors
12
168
Chapter 12: Vectors
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Vectors on the TI-86
A vector is a one-dimensional array, arranged in either one row or one column. The vector
elements can be real or complex. You can create, display, and edit vectors on the home screen
or in the vector editor. When you create a vector, the elements are stored to the vector name.
The TI
-
86 vector editor displays a vector vertically. On the home screen, a vector is entered
and displayed horizontally. When you use a vector in an expression, the TI
-
86 automatically
interprets the vector in the form (row vector or column vector) that is appropriate for the
expression. For example, a column vector is appropriate for the expression
matrix
¹
vector
.
On the TI
-
86, you can store up to 255 elements to a vector in rectangular form. You can use
two- or three-element vectors to define magnitude and direction in a two- or three-
dimensional space. You can express two- or three-element vectors in different forms,
depending on the type of vector.
To express a... You enter: And the TI
-
86 returns:
Two-element rectangular vector
ã
x
,
y
äã
x
y
ä
Two-element cylindrical vector
ã
r
±
q
äã
r
±
q
ä
Two-element spherical vector
ã
r
±
q
äã
r
±
q
ä
Three-element rectangular vector
ã
x
,
y
,
z
äã
x y z
ä
Three-element cylindrical vector
ã
r
±
q
,
z
äã
r
±
q
z
ä
Three-element spherical vector
ã
r
±
q
±
f
äã
r
±
q
±
f
ä
Chapter 12: Vectors
169
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Creating, Storing, and Displaying Vectors
The VECTR (Vector) Menu
-
Š
NAMES EDIT MATH OPS CPLX
vector vector complex
names menu math menu vector menu
vector vector
editor operations menu
The VECTR NAMES Menu
-
Š
&
The
VECTR
NAMES
menu contains all currently stored vector names in alphanumeric order.
To paste a vector name to the current cursor location, select it from the menu.
Creating a Vector in the Vector Editor
-
Š
'
Display the vector
Name=
prompt screen.
ALPHA-lock is on. The
VECTR
NAMES
menu
is displayed. Enter a name from one to eight
characters long, starting with a letter.
-
Š
'
ã
V
ä
ã
E
ä
ã
C
ä
ã
T
ä
1
1
Display the vector editor. The vector editor
menu also is displayed.
Accept or change the vector
elements
dimension with an integer
1 and
255. The
vector is displayed; all elements are
0
.
b
5
b
The TI
-
86 distinguishes
between uppercase and
lowercase letters in vector
names. For example,
VECT1
,
Vect1
, and
vect1
are three
different vector names.
$
or
#
in the first column
indicates additional vector
elements.
170
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Enter each vector element value at each
vector element prompt. You can enter
expressions. To move to the next prompt,
press b or #. The vector elements are
stored to
VECT1
, which becomes a
VECTR
NAMES
menu item.
a
5
#
49
#
2
`
45
#
`
89
#
1
`
8
The Vector Editor Menu
-
Š
'
vectorName
b
INSi DELi
4
REAL
INSi
Inserts a blank element (
en=
) prompt at the cursor location; shifts current elements down
DELi
Deletes the element from the cursor location and from the vector; shifts elements up
4
REAL
Converts the displayed complex number vector to a real number vector
Creating a Vector on the Home Screen
Define the beginning of the vector with
ã
.
Enter each vector element, separating
each from the next with a comma.
Define the end of the vector with
ä
.
-
5
P
3
P
9
-
Store the vector to a vector name from one
to eight characters long, starting with a
letter. The vector is displayed horizontally
and the vector name becomes a
VECTR
NAMES
menu item.
X - n
ã
V
ä
ã
E
ä
ã
C
ä
ã
T
ä
1
1
1
b
You can enter an expression
at a vector element prompt.
To delete a vector name from
memory, use the
MEM
DELETE:VECTR
screen
(Chapter 17).
Chapter 12: Vectors
171
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Creating a Complex Vector
If any element of a vector is complex, all elements of the vector are displayed as complex.
For example, when you enter the vector
ã
1,2,(3,1)
ä
, the TI
-
86 displays
ã
(1,0) (2,0) (3,1)
ä
.
To create a complex vector from two real vectors, the syntax is:
realVector
+(0,1)
imaginaryVector
complexVectorName
realVector
contains the real part of each element and
imaginaryVector
contains the
imaginary part.
Displaying a Vector
To display a vector, paste the vector name to the home screen, and then press
b
.
To display a specific element of
vectorName
on the home screen or in a program, the syntax is:
vectorName
(
element#
)
Real two- and three-element vector results are displayed according to the current vector
mode setting:
RectV
,
CylV
, or
SphereV
(Chapter 1). You can select a vector conversion
instruction from the
VECTR
OPS
menu to override the mode setting (page 173).
Complex vectors are displayed in rectangular form only.
172
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Using a Vector in an Expression
You can enter the vector directly (for example,
35
5,10,15
ä
).
You can use
1
and
-
n
to enter a vector name’s individual characters.
You can select the vector name from the
VECTR
NAMES
menu (
-
Š
&
).
You can select the vector name from the
VARS VECTR
screen (
-
w
/
&
).
Editing Vector Dimension and Elements
Display the vector
Name=
prompt screen.
Enter the vector name. Either select it from the
VECTR
NAMES
menu or enter the characters.
Display the vector editor.
-
Š
'
&
b
Change or accept the vector dimension.
Move the cursor to any element and edit it.
Continue moving the cursor to other elements.
Save the changes and exit the vector editor.
6
b
#
#
#
22
#
#
13
.
To use
X
to change an element value on the home screen, the syntax is:
value
vectorName
(
element#
)
When you execute the
expression, the answer is
displayed as a vector.
You can use
:
,
3
, an
d
-
p
to edit matrix
elements. You also can
overwrite existing characters.
Chapter 12: Vectors
173
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The VECTR MATH Menu
-
Š
(
NAMES EDIT MATH OPS CPLX
cross unitV norm dot
cross(
vectorA
,
vectorB
)
Returns the cross product of
vectorA
and
vectorB
, both of which are real or
complex two-element or three-element vectors; expressed with variables,
cross(
ã
a,b,c
ä
,
ã
d,e,f
ä
)
returns
ã
bf
N
ce cd
N
af ae
N
bd
ä
unitV
vector
Returns a unit vector where each element of a real or complex
vector
is
divided by the vector norm
norm
vector
Returns the Frobenius norm (
G
(
real
2
+
imaginary
2
)) where the sum is over
all elements of a real or complex
vector
dot(
vectorA
,
vectorB
)
Returns the dot product of
vectorA
and
vectorB
, both of which are real or
complex vectors; expressed with variables,
dot(
ã
a,b,c
ä
,
ã
d,e,f
ä
)
returns
ad+be+cf
The VECTR OPS (Operations) Menu
-
Š
)
NAMES EDIT MATH OPS CPLX
dim Fill
4
Pol
4
Cyl
4
Sph
44
Rec li
4
vc vc
4
li
dim
vector
Returns the dimension of (or number of elements in)
vector
#ofElements
dim
vectorName
Creates a new
vectorName
of the specified length (
#ofElements
);
each element is 0
#ofElements
dim
vectorName
Redimensions
vectorName
to the specified length (
#ofElements
)
Fill(
number
,
vectorName
)
Stores a real or complex
number
to every element in
vectorName
Press
X
to enter the
symbol after
#ofElements
.
174
Chapter 12: Vectors
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For the conversion functions below, the three-element vector conversion equations for
cylindrical form
ã
r
q
z
ä
are:
x = r cos
q
y = r sin
q
z = z
The three-element vector conversion equations for spherical form
ã
r
q
are:
x = r cos
q
sin
f
y = r sin
q
sin
f
z = r cos
f
vector
4
Pol
Displays a 2-element
vector
in polar form
ã
r
±
q
ä
vector
4
Cyl
Displays a 2- or 3-element
vector
as a cylindrical vector
ã
r
±
q
0
ä
or
ã
r
±
q
z
ä
vector
4
Sph
Displays a 2- or 3-element
vector
as a spherical vector
ã
r
±
q
0
ä
or
ã
r
±
q
f
ä
complexVector
4
Rec
Displays a 2- or 3-element
complexVector
in rectangular form
ã
x y
ä
or
ã
x y z
ä
li
4
vc
list
Converts a real or complex
list
into a vector
vc
4
li vector
Converts a real or complex
vector
into a list
Complex elements are valid
only for
l
i
4
vc
and
vc
4
li
.
Chapter 12: Vectors
175
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The VECTR CPLX (Complex) Menu
-
Š
*
NAMES EDIT MATH OPS CPLX
conj real imag abs angle
conj
complexVector
Returns a vector in which each element is the complex conjugate of the
corresponding element of a
complexVector
real
complexVector
Returns a real vector in which each element is the real portion of the
corresponding element of a
complexVector
imag
complexVector
Returns a real vector in which each element is the imaginary portion of the
corresponding element of a
complexVector
abs
Vector
Returns a real vector in which each element is either the absolute value of the
corresponding element of a real
vector
or the magnitude (modulus) of the
corresponding element of a
complexVector
angle
complexVector
Returns a real vector in which each element is either
0
if the element of
complexVector
is real or the polar angle if the element of
complexVector
is
complex; polar angles are calculated as
tan
L
1
(
complex
à
real
)
adjusted by +
p
in
the second quadrant and by
L
p
in the third quadrant
176
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Using Mathematical Functions with Vectors
vectorA+vectorB
Adds each
vectorA
element to the corresponding
vectorB
element;
returns a vector of the sums
vectorA
N
vectorB
Subtracts each
vectorB
element from the corresponding
vectorA
element; returns a vector of the differences
vector
¹number
or
number
¹vector
Returns a vector that is the product of a real or complex
number
times
each element in a real or complex
vector
matrix
¹vector
Returns a vector that is the product of each
vector
element times each
matrix
element;
matrix
column dimension and
vector
dimension must be
equal
vector
à
number
Returns a vector that is the quotient of each real or complex
vector
element divided by a real or complex
number
M
vector
(negation) Changes the sign of each
vector
element
vectorA
==vectorB
Returns
1
if every corresponding element comparison is true; returns
0
if any is false
vectorA
ƒ
vectorB
Returns
1
if at least one corresponding element comparison is false
round(vector
[
,#ofDecimals
]
)
Rounds each
vector
element to 12 digits, or rounds to specified
#ofDecimals
iPart vector
Returns the integer part of each real or complex
vector
element
fPart vector
Returns the fractional part of each real or complex
vector
element
int vector
Returns the greatest integer of each real or complex
vector
element
To add or subtract two vectors,
the dimension of
vectorA
must
equal the dimension of
vectorB
.
You cannot multiply two
vectors or divide one vector
by another vector.
==
and
ƒ
are on the
TEST
menu.
round
,
iPart
,
fPart
, and
int
are on the
MATH
NUM
menu.
13MATRX.DOC TI-86, Chap 13, US English Bob Fedorisko Revised: 02/13/01 2:32 PM Printed: 02/13/01 3:03 PM Page 177 of 10
Matrices on the TI
-
86 ...................................................... 178
Creating, Storing, and Displaying Matrices...................... 178
Using Mathematical Functions with Matrices.................. 185
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Matrices
13
178
Chapter 13: Matrices
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Matrices on the TI-86
A matrix is a two-dimensional array, arranged in rows and columns. The matrix elements
can be real or complex. You can create, display, and edit matrices on the home screen or in
the matrix editor. When you create a matrix, the elements are stored to the matrix name.
Creating, Storing, and Displaying Matrices
The MATRX (Matrix) Menu
-
NAMES EDIT MATH OPS CPLX
matrix names matrix math complex matrix
menu menu menu
matrix matrix operations
editor menu
The MATRX NAMES Menu
-
&
The
MATRX
NAMES
menu contains all currently stored matrix names in alphanumeric order.
To paste a matrix name to the current cursor location, select it from the menu.
Creating a Matrix in the Matrix Editor
-
'
Display the matrix
Name=
prompt screen.
ALPHA-lock is on. The
MATRX NAMES
menu is displayed. Enter a name from one to
eight characters long, starting with a letter.
-
'
ã
M
ä
ã
A
ä
ã
T
ä
1
1
The TI
-
86 distinguishes
between uppercase and
lowercase letters in matrix
names. For example,
MAT1
and
mat1
are two different
vector names.
Chapter 13: Matrices
179
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Display the matrix editor and the matrix
editor menu.
Accept or change the matrix dimensions
(
row
×
column
) in the top-right corner of
the screen, (1
row
255 and
1
column
255); maximum combination is
subject to memory availability. The matrix
is displayed; all elements are
0
.
b
10
b
4
b
Enter each matrix element value at the
element prompt (
1,1
=
for row 1, column 1).
You can enter expressions. To move to the
next element, press b. To move to the
next row, press #.
a
4
b
5
b
9
b
6
b
1
b
a
3
b
7
b and so on
The Matrix Editor Menu
-
'
matrixName
b
INSr DELr INSc DELc
4
REAL
INSr
Inserts a row at the cursor location; shifts subsequent rows down
DELr
Deletes row at the cursor location; shifts subsequent rows up
INSc
Inserts a column at the cursor location; shifts subsequent columns to the right
DELc
Deletes the column at the cursor location; shifts subsequent columns to the left
4
REAL
Converts the displayed complex number matrix to a real number matrix
An ellipsis (…) at either end
of matrix rows indicates
additional columns.
$
or
#
in the last column
indicates additional rows.
180
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Creating a Matrix on the Home Screen
Define the start of the matrix with
ã
, and then
define the start of the first row with another
ã
. Enter each element for the row, separating
them with commas. Define the end of the
first row with
ä
.
- -
2
P
4
P
6
P
8
-…
Define the start of each subsequent row with
ã
. Enter the row elements, separating each
from the next with a comma. Define the end
of each row with
ä
. Then define the end of
the matrix with
ä
.
- a
1
P
a
3
P a
5
P
a
7
-
-…
Store the matrix to a matrix name. Either
enter a name from one to eight characters
long, starting with a letter, or select a name
from the
MATRX
NAMES
menu. The matrix
is displayed. If newly created, the matrix
name becomes a
MATRX NAMES
menu item.
X - n
ã
M
ä
ã
A
ä
ã
T
ä
1 1
1
b
Creating a Complex Matrix
If any matrix element is complex, all elements of the matrix are displayed as complex. For
example, when you enter the matrix
[[1,2][5,(3,1)]]
, the TI
-
86 displays
[[(1,0) (2,0)][(5,0) (3,1)]]
.
To create a complex matrix from two real matrices with the same dimensions, the syntax is:
realMatrix
+(0,1)
imaginaryMatrix
complexMatrixName
realMatrix
contains the real part of each element and
imaginaryMatrix
contains the
imaginary part of each element.
The close bracket is not
necessary when it precedes
X
.
To delete a matrix name from
memory, use the
MEM
DELETE:MATRX
screen
(Chapter 17).
Chapter 13: Matrices
181
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Displaying Matrix Elements, Rows, and Submatrices
To display an existing matrix on the home screen, enter
the matrix name’s individual characters or select it from
the
MATRX
NAMES
menu, and then press
b
. The full
value of each element is displayed. Elements with very
large values may be expressed exponentially.
To display specific elements of
matrixName
, the syntax is:
matrixName
(
row
,
column
)
To display a row of
matrixName
, the syntax is:
matrixName
(
row
)
To display a submatrix of
matrixName
, the syntax is:
matrixName
(
beginRow
,
beginColumn
,
endRow
,
endColumn
)
Using a Matrix in an Expression
You can enter the matrix directly (for example,
5¹[[2,3][3,5]]
).
You can use
1
and
-
n
to enter a matrix name’s individual characters (for
example,
MAT1¹3
).
You can select the matrix name from the
MATRX
NAMES
menu (
-
&
).
You can select the matrix name from the
VARS
MATRX
screen (
-
w
/
'
).
To view elements beyond the
current screen, use
"
,
#
,
!
, and
$
.
When you execute the
expression, the answer is
displayed as a matrix.
182
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Editing Matrices in the Matrix Editor
Display the matrix
Name=
prompt screen.
Enter the matrix name. Either select it from the
MATRX
NAMES
menu or enter the characters.
- '
ã
M
äã
A
äã
T
ä
1
1
Display the matrix editor.
Edit or accept the row dimension, and then
edit or accept the column dimension.
b
5
3 b
3
b
Move the cursor to any element and edit it.
Continue moving the cursor to other
elements.
Save the changes and leave the matrix editor.
#
45
b "
21
b
2
-
~ b
.
Editing Matrices on the Home Screen
To change a matrix element value, the syntax is:
value
matrixName
(
row
,
column
)
To change the values of an entire row of elements, the syntax is:
[
valueA
,
valueB
,...,
value n
]
matrixName
(
row
)
To change the values of part of a row, beginning at a specified column, the syntax is:
[
valueA
,
valueB
,
...
,
value n
]
matrixName
(
row
,
beginColumn
)
To change the values of a submatrix within
matrixName
, the syntax is:
[[
valueA
,
...
,
value n
]
...
[
valueA
,
...
,
value n
]]
matrixName
(
beginRow
,
beginColumn
)
You can use
:
,
3
, an
d
-
p
to edit matrix
elements. You also can
overwrite existing characters.
Chapter 13: Matrices
183
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The MATRX MATH Menu
-
(
NAMES EDIT MATH OPS CPLX
det
T
norm eigVl eigVc
4
rnorm cnorm LU cond
det
squareMatrix
Returns the determinant of
squareMatrix
matrix
T
Returns a transposed matrix; each element’s (
row,column
) coordinates switch
norm
matrix
Returns the Frobenius norm (
G
(
real
2
+
imaginary
2
)) where the sum is over
all elements of a real or complex
matrix
eigVl
squareMatrix
Returns a list of the normalized eigenvalues of a real or complex
squareMatrix
eigVc
squareMatrix
Returns a matrix containing the eigenvectors for a real or complex
squareMatrix
; each column corresponds to an eigenvalue
rnorm
matrix
(row norm) Returns the largest of the sums of the absolute values of the
elements (magnitudes of complex elements) in each row of
matrix
cnorm
Matrix
(column norm) Returns the largest of the sums of the absolute values of the
elements (magnitudes of complex elements) in each column of
matrix
LU(
matrix
,
lMatrixName
,
uMatrixName
,
pMatrixName
)
Calculates the Crout LU (lower-upper) decomposition of a real or complex
matrix
; stores the lower triangular matrix to
lMatrixName
, the upper
triangular matrix to
uMatrixName
, and the permutation matrix (which
describes the row swaps done during calculation) in
pMatrixName
cond
squareMatrix
Calculates
cnorm
squareMatrix
¹
cnorm
squareMatrix
M
1
; the closer the
product is to 1, the more stable
squareMatrix
can be expected to be in matrix
functions
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The MATRX OPS (Operations) Menu
-
)
NAMES EDIT MATH OPS CPLX
dim Fill ident ref rref
4
aug rSwap rAdd multR mRAdd
4
randM
dim
matrix
Returns the dimensions of
matrix
as a list
{
rows columns
}
{
rows
,
columns
}
dim
matrixName
Creates a new
matrixName
of the specified dimensions; each
element is 0
{
rows
,
columns
}
dim
matrixName
Redimensions
matrixName
to the specified dimensions
Fill(
number
,
matrixName
)
Stores a real or complex
number
to each
matrixName
element
ident
dimension
Returns the square identity matrix of
dimension
×
dimension
ref
matrix
Returns the row-echelon form of
matrix
rref
matrix
Returns the reduced row-echelon form of
matrix
aug(
matrixA
,
matrixB
)
Concatenates
matrixA
and
matrixB
aug(
matrix
,
vector
)
Concatenates
matrix
and
vector
rSwap(
matrix
,
rowA
,
rowB
)
Returns a matrix after swapping
rowA
and
rowB
of
matrix
rAdd(
matrix
,
rowA
,
rowB
)
Returns
matrix
with (
rowA
+
rowB
) of
matrix
stored in
rowB
multR(
number
,
matrix
,
row
)
Returns
matrix
with (
row
¹
number
) stored in
row
mRAdd(
number
,
matrix
,
rowA
,
rowB
)
Returns
matrix
with ((
rowA
¹
number
)+
rowB
) stored in
rowB
randM(
rows
,
columns
)
Creates a matrix of specified dimensions with random elements
Press
X
to enter the
symbol after the close brace.
When you use
aug(
, the
number of rows in
matrixA
must equal the number of
rows in
matrixB
or the
number of elements in
vector
.
Elements of matrices created
with
randM(
are integers
‚L
9
and
9.
Chapter 13: Matrices
185
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The MATRX CPLX (Complex ) Menu
-
*
NAMES EDIT MATH OPS CPLX
conj real imag abs angle
conj
complexMatrix
Returns a matrix in which each element is the complex conjugate of the
corresponding element of a
complexMatrix
real
complexMatrix
Returns a real matrix in which each element is the real portion of the
corresponding element of a
complexMatrix
imag
complexMatrix
Returns a real matrix in which each element is the imaginary portion of
the corresponding element of a
complexMatrix
abs
matrix
Returns a real matrix in which each element is either the absolute value
of the corresponding element of a real
matrix
or the magnitude
(modulus) of the corresponding element of a complex
matrix
angle
complexMatrix
Returns a real matrix in which each element is either
0
if the element of
complexMatrix
is real or the polar angle if the element of
complexMatrix
is complex; the polar angles are calculated as
tan
L
1
(
imaginary
/
real
)
adjusted by +
p
in the second quadrant and by
L
p
in the third quadrant
Using Mathematical Functions with Matrices
matrixA
+
matrixB
Adds each
matrixA
element to the corresponding
matrixB
element;
returns a matrix of the sums
matrixA
N
matrixB
Subtracts each
matrixB
element from the corresponding
matrixA
element; returns a matrix of the differences
To add or subtract two
matrices, the dimensions of
matrixA
must equal the
dimensions of
matrixB
.
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matrixA¹matrixB
or
matrixB
¹matrixA
Multiplies
matrixA
and
matrixB
; returns a square matrix of the
products
matrix
¹number
or
number
¹matrix
Returns a matrix that is the product of a real or complex
number
times each element in a real or complex
matrix
matrix
¹vector
Returns a vector that is the product of each
vector
element times each
matrix
element; the
matrix
column dimension and
vector
dimension
must be equal
M
matrix
(negation) Changes the sign of each element in
matrix
squareMatrix
M
1
Returns the inverse of
squareMatrix
(not the inverse of each element)
matrix
2
Squares a square matrix
squareMatrix
^
power
Raises a
squareMatrix
to the designated
power
e^
squareMatrix
Returns the square matrix exponential of a real
squareMatrix
sin
squareMatrix
Returns the square matrix sine of a real
squareMatrix
cos
squareMatrix
Returns the square matrix cosine of a real
squareMatrix
matrixA
==
matrixB
Returns
1
if every corresponding element comparison is true; returns
0
if any is false
matrixA
ƒ
matrixB
Returns
1
if at least one corresponding element comparison is false
round(
matrix
[
,
#ofDecimals
]
)
Rounds each
matrix
element to 12 digits or to specified
#of Decimals
iPart
matrix
Returns the integer part of each element of a real or complex
matrix
fPart
matrix
Returns the fractional part of each element of a real or complex
matrix
int
matrix
Returns the greatest integer of each element of a real or complex
matrix
To multiply two matrices, the
column dimension of
matrixA
must equal the row
dimension of
matrixB
.
To enter
M
1
, press
-
ƒ
. Do
not use
2
@
a
1
.
e^
,
sin
, and
cos
do not return
the exponential, sine, or
cosine of each matrix
element.
To make relational
comparisons,
matrixA
and
matrixB
must have equal
dimensions.
==
and
ƒ
are on the
TEST
menu.
round
,
iPart
,
fPart
, and
int
are on the
MATH
NUM
menu.
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Statistical Analysis on the TI
-
86 ......................................188
Setting Up a Statistical Analysis....................................... 188
Results of a Statistical Analysis........................................ 192
Plotting Statistical Data ...................................................194
The STAT DRAW Menu .................................................... 199
Forecasting a Statistical Data Value ................................199
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
14
Statistics
188
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Statistical Analysis on the TI-86
With the TI
-
86, you can analyze one-variable and two-variable statistical data, which are
stored in lists. One-variable data has one measured variable. Two-variable data has pairs
comprising an independent variable and a dependent variable.
When analyzing either kind of data, you can specify a frequency of occurrence for the
independent variable values. These specified frequencies must be real numbers
0.
Setting Up a Statistical Analysis
Enter the statistical data into one or more lists (Chapter 11).
Calculate the statistical variables or fit a model to the data.
Plot the data.
Graph the regression equation for the plotted data.
The STAT (Statistics) Menu
-
š
CALC EDIT PLOT DRAW VARS
4
FCST
statistical stat plot statistical result
calculations menu variables menu
menu list editor statistical drawing forecast
tools menu editor
The same list editor is
displayed, whether you press
-
š
'
or
-
)
.
For a description of the list
editor, see Chapter 11.
Chapter 14: Statistics
189
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Entering Statistical Data
Data for statistical analysis is stored in lists, which you can create and edit in the list editor
(Chapter 11), on the home screen (Chapter 11), or in a program (Chapter 16). The TI
-
86 has
three built-in list names for statistics,
xStat
(x-variable list),
yStat
(y-variable list), and
fStat
(frequency list). TI
-
86 statistical functions use these lists as defaults.
The LIST NAMES Menu
-
š
'
(
{ } NAMES EDIT OPS
fStat xStat yStat
fStat
An automatically updated list of the frequency values used in the last statistical
computation requiring a frequency; default is a list where each element is
1
xStat
An automatically updated list of the data from the x-list used in the last statistical analysis
yStat
An automatically updated list of the data from the y-list used in the last statistical analysis
The STAT CALC (Calculations) Menu
-
š
&
CALC EDIT PLOT DRAW VARS
OneVa TwoVa LinR LnR ExpR
4
PwrR SinR LgstR P
2
Reg P
3
Reg
4
P
4
Reg StReg
OneVa
(one variable) Analyzes data with one measured variable
TwoVa
(two variable) Analyzes paired data
The
LIST
NAMES
menu
shown here has no user-
created list names.
Editing an element of
xStat
o
r
yStat
clears any values
stored to statistical result
variables.
The
STAT
CALC
functions
store the results to statistical
result variables (page 193 ).
The syntax description for
each
STAT
CALC
menu item
follows this section.
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LinR
(linear regression) Fits the model equation y=a+bx to the data; displays values for
a
(slope) and
b
(y-intercept)
LnR
(logarithmic regression) Fits the model equation y=a+b ln x to the data using transformed
v
alues ln(x) and y; displays values for
a
and
b
ExpR
(exponential regression) Fits the model equation y=ab
x
to the data using transformed
v
alues x and ln(y); displays values for
a
and
b
; elements in the x-list and y-list elements
must be integers
PwrR
(power regression) Fits the model equation y=ax
b
to the data using transformed values
ln(x) and ln(y); displays values for
a
and
b
SinR
(sinusoidal regression) Fits the model equation y=a¹sin(bx+c)+d to the data; displays
v
alues for
a
,
b
,
c
, and
d
;
SinR
requires at least four data points; it also requires at least
two data points per cycle to avoid aliased frequency estimates
LgstR
(logistic regression) Fits the model equation y=a
à
(1+be
cx
)+d to the data; displays
a
,
b
,
c
, and
d
P
2
Reg
(quadratic regression) Fits the second-degree polynomial y=ax
2
+bx+c to the data;
displays values for
a
,
b
, and
c
; for three data points, the equation is a polynomial fit; for
four or more, it is a polynomial regression;
P
2
Reg
requires at least three data points
P
3
Reg
(cubic regression) Fits the third-degree polynomial y=ax
3
+bx
2
+cx+d to the data; displays
v
alues for
a
,
b
,
c
, and
d
; for four points, the equation is a polynomial fit; for five or more, it
is a polynomial regression;
P
3
Reg
requires at least four data points
P
4
Reg
(quartic regression) Fits the fourth-degree polynomial y=ax
4
+bx
3
+cx
2
+dx+e to the data;
displays values for
a
,
b
,
c
,
d
, and
e
; for five points, the equation is a polynomial fit; for six
or more, it is a polynomial regression;
P
4
Reg
requires at least five data points
StReg
(store regression equation) Pastes
StReg(
to the home screen; enter a
variable
and press
b; the current regression equation is stored to
variable
For regression analysis, the
statistical results are
calculated using a least-
squares fit.
SinR
and
LgstR
are
calculated using an iterative
least-squares fit.
Chapter 14: Statistics
191
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For
OneVa
, the syntax is:
OneVar
ãxList,frequencyListä
For
TwoVa
, the syntax is:
TwoVar
ã
xLlist,yList,frequencyList
ä
For
LinR
,
LnR
,
ExpR
,
PwrR
,
P2Reg
,
P3Reg
, and
P4Reg
, the syntax is:
TwoVar
ãxList,yList,frequencyListä
For
SinR
, the syntax is:
SinR
ãiterations,xList,yList,period,equationVariableä
iterations
is the number of iterations to go through; higher values for iterations produce a
better fit, but take longer to calculate.
period
is an initial guess at which to begin calculation.
For
LgstR
, the syntax is:
LgstR
ãiterations,xList,yList,frequencyList,equationVariableä
To copy the contents
RegEq
to any variable after calculating the regression, the syntax is:
StReg(variable)
Automatic Regression Equation Storage
LinR
,
LnR
,
ExpR
,
PwrR
,
SinR
,
LgstR
,
P2Reg
,
P3Reg
, and
P4Reg
are regression models. Each
regression model has an optional argument,
equationVariable
, for which you can specify an
equation variable, such as
y1
. Upon execution, the regression equation is stored
automatically to the specified equation variable, and the function is selected.
Regardless of whether you specify
equationVariable
, the regression equation always is
stored to the result variable
RegEq
, which is an item on the
STAT
VARS
menu. The
regression equation displays the actual result values.
When you select
OneVa
or
TwoVa
, the abbreviation
OneVar
or
TwoVar
is
displayed.
For
PwrR
and
ExpR
, the
elements of
xList
and
yList
must be integers
1.
Default for
iterations
is 64.
192
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The result for a polynomial regression, sinusoidal regression, or logistic regression is stored in
PRegC
(polynomial
à
regression coefficients).
PRegC
is a list containing the coefficients for an
equation. For example, for
P3Reg
, the result
PRegC={3 5
L
2 7}
would represent
y=3x
3
+5x
2
N
2x+7.
Results of a Statistical Analysis
When you perform a statistical analysis, the calculated results are stored in the result
variables and the data from the lists used in the analysis are stored to
xStat
,
yStat
, and
fStat
.
If you edit a list or change the type of analysis, all statistical variables are cleared.
The STAT VARS (Statistical Variables) Menu
-
š
*
CALC EDIT PLOT DRAW VARS
vs
xSx
ws
y
4
Sy
G
x
G
x
2
G
y
G
y
2
4G
xy RegEq corr a b
4
n minX maxX minY maxY
4
Med PRegC Qrtl1 Qrtl3 tolMe
To paste a result variable to the cursor location, either select the variable from the
STAT
VARS
menu or select the variable from the
VARS STAT
selection screen.
To use a result variable in an expression, paste it to the appropriate cursor location.
To display the value of a result variable, paste it to the home screen and press
b
.
To store results to another variable after a calculation, paste the result variable to the
home screen, press
X
, enter a new variable, and then press
b
.
PRegC
is the only statistical
result variable calculated for
a polynomial regression.
One- and two-variable
statistical functions share the
result variables.
The statistical variables are
calculated and stored as
shown in the table on the
next page.
You can use ALPHA keys,
alpha keys, and the
CHAR
GREEK
menu to enter some
result variables.
Chapter 14: Statistics
193
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Result
Variables
1-Var
Stats
2-Var
Stats Other
Result
Variables
1-Var
Stats
2-Var
Stats Other
mean of x values
vv
correlation coeff
corr
pop std dev of x
s
x
s
x
y-intercept of reg eq
a
sample std dev of x
Sx Sx
slope of reg eq
b
mean of y values
w
regression
à
fit coeff
a
,
b
pop std dev of y
s
y
number of data pts
nn
sample std dev of y
Sy
min of x values
minX minX
sum of x values
G
x
G
x
max of x values
maxX maxX
sum of x
2
values
G
x
2
G
x
2
min of y values
minY
sum of y values
G
y
max of y values
maxY
sum of y
2
values
G
y
2
median
Med
sum of x ¹ y
G
xy
1st quartile
Qrtl1
regression equation
RegEq
3rd quartile
Qrtl3
polynomial,
LgstR
,
and
SinR
coeff’s
a
(y-int)
b
(slope)
polynomial
LgstR
,
and
SinR
reg coeff’s
PRegC
The first quartile (
Qrtl1
) is the median of the points between
minX
and
Med
(median). The
third quartile (
Qrtl3
) is the median of the points between
Med
and
maxX
.
When you calculate a logistic regression,
1
is stored to
tolMet
(
tolMe
) if the TI
-
86 internal
tolerance was met before the calculator arrived at a result; if not met,
0
is stored to
tolMet
.
These words are abbreviated
in the table:
pop = population
std dev = standard deviation
coeff = coefficient
int = intercept
reg eq = regression equation
pts = points
min = minimum
max = maximum
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Plotting Statistical Data
You can plot one, two, or three sets of statistical list data. The five available plot types are
scatter plot, xyLine, histogram, modified box plot, and regular box plot.
Store the statistical data in one or more lists (Chapter 11).
Select or deselect functions in the current equation editor as appropriate (Chapter 5).
Define the statistical plot.
Turn on the plots you want to display.
Define the window variables for the graph screen (Chapter 5).
Display and explore the plotted graph (Chapter 6).
The STAT PLOT Status Screen
-
š
(
The
STAT
PLOT
status screen summarizes the settings for
Plot1
,
Plot2
, and
Plot3
. The
illustration below identifies the settings for
Plot1
. This screen is not interactive. To change a
setting, select
PLOT1
,
PLOT2
, or
PLOT3
from the
STAT
PLOT
status screen menu.
Stat plot name On
à
Off status
1:Plot1...
O
ff
Plot-type icon
®
xStat
yStat
Mark-type icon
Independent list name Dependent list name
This screen shows the
default stat plot settings. If
you select another plot type,
some prompts may change.
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The STAT PLOT Menu
-
š
(
PLOT1 PLOT
2
PLOT
3
PlOn PlOff
PLOT1
Displays the stat plot editor for
Plot1
PLOT2
Displays the stat plot editor for
Plot2
PLOT3
Displays the stat plot editor for
Plot3
PlOn
[
1,2,3
] Turns on all plots (if you enter no arguments) or turns on specified plots only
PlOff
[
1,2,3
] Turns off all plots (if you enter no arguments) or turns off specified plots only
To turn on or turn off all three stat plots, select
PlOn
or
PlOff
from the
STAT
PLOT
menu.
PlOn
or
PlOff
is pasted to the home screen. Press
b
. All stat plots are now on or off.
Setting Up a Stat Plot
To set up a stat plot, select
PLOT1
,
PLOT2
, or
PLOT3
from
the
STAT
PLOT
menu. The stat plot editor for the selected
stat plot is displayed. Each stat plot type has a unique stat
plot editor. The screen to the right shows the stat plot
editor for the default
®
(scatter plot). If you select
another plot type, some prompts may change.
Turning On and Turning Off a Stat Plot
When you display a stat plot editor, the cursor is on the
On
option.
To turn on the stat plot, press
b
.
To turn off the stat plot, press
"
b
.
When you display a stat plot
editor, the
STAT
PLOT
menu
remains so that you can
easily switch to another stat
plot.
In this guidebook, brackets
(
ã
and
ä
)
with syntax specify
arguments as optional. Do
not enter brackets, except
with vectors and matrices.
You need not turn on a stat
plot to change the settings.
You also can use
STAT
PLOT
menu items
PlOn
or
PlOff
to
turn on or turn off stat plots.
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The PLOT TYPE Menu (Selecting a Plot Type)
PLOT1 PLOT2 PLOT3 PlOn PlOff
SCAT xyLINE MBOX HIST BOX
At this prompt... Enter this information: Default is: Displayed menu is:
Xlist Name=
independent-data list name
xStat
LIST
NAMES
menu
Ylist Name=
dependent-data list name
yStat
LIST
NAMES
menu
Freq=
frequency list name (or
1
)
fStat
(default value:
1
)
LIST
NAMES
menu
Mark=
plot mark (
or
+
or
¦
)
(none for
HIST
or
BOX
)
PLOT MARK
menu
Any list you enter at the
Xlist Name=
prompt is stored to the list name
xStat
.
Any list you enter at the
Ylist Name=
prompt is stored to the list name
yStat
.
Any list you enter at the
Freq=
prompt is stored to
fStat
.
Plot Type Characteristics
®
SCAT
(scatter plot) plots the data points from
Xlist Name
and
Ylist Name
as coordinate
pairs, representing each point with a box (
), cross (
+
), or dot (
¦
) mark type.
Xlist Name
and
Ylist Name
must be the same length.
Xlist Name
and
Ylist Name
can be the same list.
For the example:
xStat={1 2 3 4 5 6 7 8 9 10}
yStat=5 sin(xStat)
Window variable values:
xMin=0
yMin=
L
10
xMax=10
yMax=10
To display the
PLOT
TYPE
menu, move the cursor onto
the plot type icon at the
Type=
prompt.
When you select a plot type,
the appearance of the stat
plot editor may change.
Stat plots are displayed on
the graph screen
(
6
*
)
,
as defined by the window
variable values (Chapter 5).
Some graph tools apply to
stat plots.
In these stat plot examples,
all functions are deselected.
Also, menus are cleared from
the screen with
:
.
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xyLINE
is a scatter plot in which the data points are plotted and connected in order of
appearance in
Xlist Name
and
Ylist Name
. You may want to use
SortA
or
SortD
from the
LIST
OPS
menu (Chapter 11) to sort the lists before you plot them.
For the example:
xStat={1 2 3 4 5 6 7 8 9 10}
yStat=5 sin(xStat)
Window variable values:
xMin=0
yMin=
L
10
xMax=10
yMax=10
¯
MBOX
(modified
box plot) plots one-variable data, like the regular box plot, except that
the points are 1.5
¹
Interquartile Range beyond the quartiles. (The Interquartile Range is
defined as the difference between the third quartile
Q
3
and the first quartile
Q
1
.) These
points are plotted individually beyond the whisker, using the
Mark
(
or
+
or
¦
) you select.
For the example:
xStat={1 2 2 2.5 3 3.3 4 4 2 6 9}
Window variable values are
set by selecting
ZDATA
from
the
GRAPH
ZOOM
menu.
You can trace these points, which are called outliers. When outliers exist, the end of each
whisker will display an
x=
prompt. When no outliers exist,
xMin
and
xMax
are the prompts for
the end of each whisker.
Q
1
,
Med
(median), and
Q
3
define the box.
Modified box plots are plotted with respect to
xMin
and
xMax
, but ignore
yMin
and
yMax
.
When two modified box plots are plotted, the first one plots at the top of the screen and the
Whiskers are the lines
protruding from the sides of
the box.
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second plots in the middle. When three are plotted, the first one plots at the top, the second
in the middle, and the third at the bottom.
¬
HIST
(histogram) plots one-variable data. The
xScl
window variable value determines
the width of each bar, beginning at
xMin
.
ZDATA
(
GRAPH
ZOOM
menu) adjusts
xMin
,
xMax
,
yMin
, and
yMax
to include all values, and also adjusts
xScl
. (
xMax
N
xMin
)
à
xScl
47 must be
true. A value that occurs on the edge of a bar is counted in the bar to the right.
For the example:
xStat={1 2 2 2 3 8 9 5 6 6 7 7
4 4 9 9 9}
Window variable values:
xMin=0
yMin=0
xMax=10
yMax=5
°
BOX
(regular box plot) plots one-variable data. The whiskers on the plot extend from
the minimum data point in the set (
xMin
) to the first quartile (
Q
1
) and from the third quartile
(
Q
3
) to the maximum point (
xMax
). The box is defined by
Q
1
,
Med
(median), and
Q
3
.
For the example:
xStat={1 2 2 2.5 3 3.3 4 4 2 6 9}
Window variable values are
set by selecting
ZDATA
from
the
GRAPH
ZOOM
menu.
Box plots are plotted with respect to
xMin
and
xMax
, but ignore
yMin
and
yMax
. When two
box plots are plotted, the first one plots at the top of the screen and the second plots in the
Whiskers are the lines
protruding from the sides of
the box.
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middle. When three are plotted, the first one plots at the top, the second in the middle, and
the third at the bottom.
The STAT DRAW Menu
-
š
)
CALC EDIT PLOT DRAW VARS
HIST SCAT xyLINE BOX MBOX
4
DRREG CLDRW DrawF STPIC RCPIC
HIST
Draws a histogram of one-variable data
SCAT
Draws a scatter plot of the data points
xyLINE
Draws the data points and a line connecting each point to the next point
BOX
Draws a box plot of the data points
MBOX
Draws a modified box plot of the data points
DRREG
(draw regression equation) Draws the current regression equation
CLDRW
(clear drawings) Displays the current graph with no drawings
DrawF
expression
(draw function) Plots
expression
as a drawing
STPIC
(store picture) Displays the picture variable
Name=
prompt; enter a valid variable
name, starting with a letter, and then press
b
to store the current picture
RCPIC
(recall picture) Displays the picture variable
Name=
prompt and menu; select or
enter a valid variable name, and then press
b
; the stored picture is redrawn
Forecasting a Statistical Data Value
Using the forecast editor, you can forecast an x-value or y-value based on the current
regression equation. To use the forecast editor, a regression equation must be stored to
RegEq
.
When you select any of the
first five
STAT
DRAW
menu
items, the TI
-
86 plots the
data stored in the lists
xStat
and
yStat
.
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Enter stat data in the list editor. The screen to
the right shows all
fStat
elements as
1
, but you
need not enter them.
1
is the default for all
fStat
elements. However, if other elements are
stored to
fStat
, you must clear them.
- š '
`
1
#
1
`
1
#
2
#
4
#
5
# "
1
#
2
#
3
#
4
#
2
Display the home screen.
Execute a linear regression for
xStat
and
yStat
.
The statistical results are displayed.
Remove the
STAT
CALC
menu to display all
results, including
n
.
.
- š &
( b
.
Display the forecast editor. The current
regression model is displayed on the top line.
Enter
x=3
, and then move the cursor to the
y=
prompt.
/ &
3
#
Select
SOLVE
from the forecast editor menu to
solve for
y
at
x=3
. A small square indicates the
solution. You can continue to use the forecast
editor with other values for
x
or
y
.
*
When you use
FCST
, the values of
x
,
y
, and
Ans
are not updated. To store the
x
value or
y
value, move the cursor onto the variable to be stored, press
X
, enter a valid variable
name at the
Sto
prompt, and then press
b
.
Values entered at forecast
editor prompts must be real
numbers or expressions that
evaluate to real numbers.
If the most recent calculation
was a polynomial regression,
you can only forecast the
y
value.
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Preview: The Equation Solver .......................................... 202
Entering an Equation in the Equation-Entry Editor .......... 203
Setting Up the Interactive-Solver Editor........................... 204
Solving for the Unknown Variable ...................................206
Graphing the Solution...................................................... 207
Solver Graph Tools........................................................... 207
The Simultaneous Equation Solver .................................. 208
The Polynomial Root-Finder............................................. 211
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
15
Equation Solving
202
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Preview: The Equation Solver
-
t
With the equation solver, you can enter an expression or equation, store values to all but
one variable in the expression or equation, and then solve for the unknown variable. These
steps introduce the solver. For details, read this chapter.
Display the equation-entry editor. The
VARS
EQU
menu is displayed on the
bottom of the screen.
Enter an equation. When you press
b
, the interactive-solver editor and
solver menu are displayed.
-
t
1
ã
V
ä
1
1
ã
=
ä
1
ã
V
ä
D
1
ã
R
ä
1
F
D
1
ã
R
ä
1
\
1
ã
R
ä
2
E
E
b
Enter values for each variable, except the
unknown variable
R1
. Some variables
may have values stored to them already.
Move the cursor to the variable for which
you want to solve. You may enter a guess.
10
#
100
#
#
57
$
Solve the equation for the variable. Small
squares mark both the solution variable
and the equation
left
N
rt=0
(the left side of
the equation minus the right side of the
equation). If you edit a value or leave the
screen, the squares disappear.
*
The
VARS
EQU
menu is a
menu version of the
VARS
EQU
screen (Chapter 2).
The example uses a formula
for a voltage divider.
R1
and
R2
represent
resistors.
V
and
V1
represent voltage.
To solve for the unknown
variable in an equation on the
home screen or in the
program editor, select
Solver(
from the
CATALOG
(A to Z
Reference).
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Entering an Equation in the Equation-Entry Editor
The equation solver uses two editors: the equation-entry editor, where you enter and edit the
equation you want to solve, and the interactive-solver editor, where you enter known variable
values, select the variable for which you want to solve, and display the solution.
To display the equation-entry editor, press
-
t
. In
this editor, you can:
Enter an equation directly.
Enter a defined equation variable’s individual
characters or select it from the
VARS
EQU
menu.
Recall the contents of a defined equation variable.
As you enter or edit the equation, the TI
-
86 automatically stores it to the variable
eqn
.
The
VARS
EQU
menu is a menu version of the
VARS
EQU
screen (Chapter 2). The items are
all variables to which an equation is stored. This includes all selected and deselected
equation variables defined in the equation editors of all four graphing modes (Chapters 5, 8,
9, and 10). The menu items are in alphanumeric order.
If you select an equation variable from the menu, the variable is pasted to the cursor
location, overwriting characters for the length of the variable name.
If you press
-
, select an equation variable from the menu, and then press
b
,
the variable contents are inserted at the cursor location.
If you enter an equation variable, the TI
-
86 automatically converts it to the equation
exp=
equationVariable
. If you enter an expression directly, the TI
-
86 automatically converts
the expression to the equation
exp=
expression
.
The equation can have more
than one variable to the left o
f
the equal sign, as in
A+B=C+sin D
.
You can display other menus
in the equation-entry editor.
An ellipsis (...) indicates that
an entered equation
continues beyond the screen.
To move directly to the start
of the equation, press
-
!
;
to move directly to the end,
press
-
"
.
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Setting Up the Interactive-Solver Editor
After you have stored an equation to
eqn
in the equation-entry
editor, press
b
to display the interactive-solver editor.
The equation is displayed across the top of the editor.
Each variable in the equation is displayed as a prompt.
Values already stored to variables are displayed; undefined
variables are blank. The solver menu is displayed on the
bottom of the editor (page 206).
bound={
L
1E99,1E99}
is a list containing the default lower bound (
L
1E99
) and the default upper
bound (
1E99
). You can edit the bounds (below).
Entering Variable Values
To solve for an unknown variable, you must define every other variable in the equation.
When you enter or edit a variable value in the interactive-solver editor, the new value is
stored to the variable in memory. For any variable, you may enter an expression, which is
evaluated when you press
b
,
#
,
$
, or
.
. Expressions must resolve to real numbers
at each step of the calculation.
Controlling the Solution with Bounds and a Guess
The solver seeks a solution only within the specified bounds. Whenever you display the
interactive-solver editor, the default
bound={
L
1E99,1E99}
is displayed. These are the
maximum bounds for the TI
-
86.
In the example, the equation
V1=V(R1
à
(R1+R2))
was
entered in the equation-entry
editor.
If you entered an expression
for
eqn
, then
exp=
is the first
variable prompt on the
interactive-solver editor.
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The TI
-
86 solves equations through an iterative process. To control that process, you can
enter lower bounds and upper bounds that are close to the solution, and enter a guess
within those bounds in the prompt for the unknown variable.
Controlling the process with specific bounds and a guess helps the TI
-
86 in two ways.
It finds a solution more quickly.
It is more likely to find the solution you want when an equation has multiple solutions.
To set more precise bounds at the
bound=
prompt, the syntax is:
bound={
lowerBound
,
upperBound
}
At the prompt for the unknown variable, you may enter a guess or a list of two guesses. If
you do not enter a guess, the TI
-
86 uses (
lowerBound
+
upperBound
)
à
2 as a guess.
On the solver graph (page 207), you can guess a solution by moving the free-moving cursor
or trace cursor to a point on the graph between
lowerBound
and
upperBound
. To solve for
the unknown variable using the new guess, select
SOLVE
from the solver graph menu. The
solution is displayed on the interactive-solver editor.
Editing the Equation
To edit the equation stored to
eqn
when the interactive-solver editor is displayed, press
$
until the cursor is on the equation. The equation-entry editor is displayed. The TI
-
86
automatically stores the edited equation to
eqn
as you edit.
If you store an equation to
eqn
by recalling the contents of an equation variable, such as
y1
,
and then edit the equation stored to
eqn
, the original equation (in
y1
, for example) is not
changed. Likewise, subsequently editing the contents of the equation variable (
y1
, for
example) does not change
eqn
.
lowerBound
<
upperBound
must be true.
You can enter a list variable
at the
bound=
prompt if a
valid two-element list is
stored to it.
If you exit the equation
solver, any equation stored t
o
eqn is displayed when you
return to the equation solver.
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The Solver Menu
-
t
equation
b
GRAPH WIND ZOOM TRACE SOLVE
graphs the solver zoom solves for the unknown variable or
equation in
eqn
menu displays the interactive-solver editor
window graphs
eqn
and
editor activates the trace cursor
To display the window editor, select
WIND
from the solver menu.
When you select
GRAPH
or
WIND
from the solver menu,
EDIT
replaces the item you selected on
the menu. To return to the interactive-solver editor from the graph or window editor, select
EDIT
.
Solving for the Unknown Variable
After you have stored all known variable values, set the bounds, and entered a guess
(optional), move the cursor to the prompt for the unknown variable.
To solve, select
SOLVE
from the solver menu (
*
).
A small square marks the variable for which you
solved. The solution value is displayed.
A small square also marks the
left
N
rt=
prompt. The
value at this prompt is the value of the left side of the
equation minus the value of the right side of the
equation, evaluated at the new value of the variable
for which you solved. If the solution is precise,
left
N
rt=0
is displayed.
Some equations have more than one solution. To look for additional solutions, you can
enter a new guess or set new bounds, and then solve for the same variable.
You can display other menus
in the interactive-solver editor
An ellipsis (...) indicates that
the variable value continues
beyond the screen. To scroll
the value, press
"
and
!
.
The squares disappear when
you edit any value.
After solving, you can edit a
variable value or edit the
equation, and then solve for
the same variable or another
variable in the equation.
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Graphing the Solution
When you select
GRAPH
from the solver menu (
&
), the
solver graph is displayed with the free-moving cursor.
The vertical axis represents the result of the left side
of the equation minus the right side of the equation
(left
N
right) at each independent variable value.
The horizontal axis represents the independent
variable for which you solved the equation.
On the graph, solutions exist for the equation where
left
N
rt=0
, which is where the graph
intersects the x-axis. The solver graph:
Uses the current window and format settings (Chapter 5).
Does not graph the solution according to the current graphing mode.
Always graphs a solution as a function graph.
Does not graph selected functions or turned on stat plots along with the solution.
Solver Graph Tools
You can explore the graph of a solution with the free-moving cursor, as you would on any
other graph. When you do, the coordinate values for the variable (the x-axis) and the value
left
N
rt
(the y-axis) are updated.
To activate the trace cursor, select
TRACE
from the solver menu. Panning, QuickZoom, and
entering a specific value (Chapter 6) are available with the trace cursor on the solver graph.
To return to the solver menu from a trace, press
.
.
The graph to the right plots
the solution from the example
on page 202. The window
variable values are:
xMin=
L
10
yMin=
L
50
xMax=50
yMax=50
You can use the free-moving
cursor or trace cursor to
select a guess on the graph.
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The Solver ZOOM Menu
-
t
equation
b
(
GRAPH
WIND
ZOOM TRACE SOLVE
BOX ZIN ZOUT ZFACT
ZSTD
BOX
Draws a box to redefine the viewing window (Chapter 6)
ZIN
Magnifies the graph around the cursor by factors of
xFact
and
yFact
(Chapter 6)
ZOUT
Displays more of the graph around the cursor by factors of
xFact
and
yFact
(Chapter 6)
ZFACT
Displays the
ZOOM
FACTORS
screen (Chapter 6)
ZSTD
Displays the graph in standard dimensions; resets the default window variable values
for
Func
graphing mode
The Simultaneous Equation Solver
-
u
The
s
imultaneous equation solver solves systems of up to 30 linear equations with 30 unknowns.
Entering Equations to Solve Simultaneously
Display the
SIMULT
number screen.
Enter an integer
2 and
30 for the
number of equations. The coefficients-
entry editor for the first equation (for a
system of
n
equations and
n
unknowns) is
displayed. The
SIMULT ENTRY
menu also
is displayed.
- u
3
b
Chapter 6 and the A to Z
Reference describe these
features in detail.
The
SIMULT
coefficients are
not variables.
You can display other menus
in the coefficients-entry
screen.
Chapter 15: Equation Solving
209
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Enter a real or complex value (or an
expression that resolves to one) for each
coefficient in the equation and for
b
1
,
which is the solution to that equation.
9
#
8
#
7
#
2
Display the coefficients-entry screen for
the second and third equation, and enter
values for them.
# (or b or
')
5
# a
6
# a
4
#
2
#
1
#
5
#
9
#
7
Solve the equations. The results of the
polynomial are calculated and displayed
on the result screen. Results are not stored
to variables and cannot be edited. The
SIMULT
RESULT
menu is displayed.
*
To move from the
coefficients-entry editor for
one equation to the editor for
another equation, select
PREV
or
NEXT
.
To move among coefficients,
press
#
,
$
, or
b
. From
the last or first coefficient,
these keys move to the next
or previous coefficients-entry
screen, if possible.
Ellipses indicate that a value
continues beyond the screen.
Press
"
and
!
to scroll the
value.
210
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Storing Equation Coefficients and Results to Variables
To store coefficients
a
1,1
;
a
1,2
;...;
a
n
,
n
to an
n
×
n
matrix, select
STOa
.
To store solutions
b
1
,b
2
,...,
b
n
to a vector of dimension
n
, select
STOb
.
To store the results
x
1
,
x
2
,...,
x
n
to a vector of dimension
n
, select
STOx
.
To store a single value on the coefficients-entry screen or result screen, follow these steps.
Move the cursor to the = sign next to the
coefficient or result you want to store.
#
Display the variable
Name=
prompt.
ALPHA-lock is on.
Enter the variable to which you want to
store the value.
Store the value. The variable name
becomes an item on the
VARS
REAL
screen or
VARS
CPLX
screen.
X
ã
R
ä
ã
E
ä
ã
S
ä
ã
U
ä
ã
L
ä
ã
T
ä
1
2
b
To return to the coefficients-entry screen, where you can edit coefficients and calculate
new solutions, select
COEFS
from the
SIMULT
RESULT
menu.
To switch to the coefficients-
entry screen, select
COEFS
from the
SIMULT
RESULT
menu.
To solve equations
simultaneously on the home
screen or in a program,
select
simult(
from the
CATALOG
.
Chapter 15: Equation Solving
211
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The Polynomial Root-Finder
-
v
The root finder solves up to 30th-order real or complex polynomials.
Entering and Solving a Polynomial
Display the
POLY
order screen.
Enter an integer between 2 and 30. The
coefficients-entry editor is displayed with the
equation across the top, the coefficient
prompts along the left side, and the
POLY
ENTRY
menu on the bottom.
-
v
4
b
Enter a real or complex value (or an expression
that resolves to one) for each coefficient.
To clear all coefficients, select
CLRa
from the
POLY
ENTRY
menu.
18
#
5
#
21
#
7
#
16
Solve the equation. The roots of the polynomial
are calculated and displayed. Results are not
stored to variables and you cannot edit them.
Also, the
POLY
RESULT
menu is displayed.
Results can be complex numbers.
*
The
POLY
coefficients are no
t
variables.
You can display other menus
in the coefficients-entry
editor.
Ellipses indicate that a value
continues beyond the screen.
Press
"
and
!
to scroll the
value.
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Storing a Polynomial Coefficient or Root to a Variable
Move the cursor to the = sign next to the
coefficient or root value you want to store.
# # #
Display the
Sto
prompt. ALPHA-lock is on.
Enter the variable to which you want to
store the value.
Store the value.
X
ã
R
ä
ã
O
ä
ã
O
ä
ã
T
ä
1
1
b
Display the
Name=
prompt for the
coefficents list name. ALPHA-lock is on.
Enter the list variable name to which you
want to store the coefficients.
Store the polynomial coefficient values.
'
ã
C
ä
ã
O
ä
ã
E
ä
ã
F
ä
1
1
b
To return to the coefficients-entry screen, where you can edit coefficients and calculate
new solutions, select
COEFS
from the
POLY
RESULT
menu.
To switch to the coefficients-
entry screen, select
COEFS
from the
POLY
RESULT
menu.
To find roots on the home
screen or in a program,
select
poly
from the
CATALOG
.
16PROG.DOC TI-86, Chap 16, US English Bob Fedorisko Revised: 02/13/01 2:36 PM Printed: 02/13/01 3:04 PM Page 213 of 16
Writing a Program on the TI-86 ....................................... 214
Running a Program..........................................................221
Working with Programs ...................................................223
Running an Assembly Language Program ....................... 225
Entering and Storing a String........................................... 226
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
16
Programming
214
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Writing a Program on the TI-86
A program is a set of expressions, instructions, or both, which you enter or download.
Expressions and instructions in the program are executed when you run the program.
You can use most TI
-
86 features in a program. Programs can retrieve and update all
variables stored to memory. Also, the program editor menu has input
à
output commands,
such as
Input
and
Disp
, and program control commands, such as
If
,
Then
,
For
, and
While
.
The PRGM Menu
8
NAMES EDIT
program program editor
names menu
Creating a Program in the Program Editor
To begin writing a program, select
EDIT
from the
PRGM
menu (
8
'
). The program
Name=
prompt and
PRGM
NAMES
menu are displayed. ALPHA-lock is on. Enter a
program name from one to eight characters long,
beginning with a letter. To edit an existing program, you
can select the name from the
PRGM
NAMES
menu.
The TI
-
86 distinguishes
between uppercase and
lowercase letters in program
names. For example,
ABC
,
Abc
, and
abc
would be three
different program names.
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215
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After you enter a program name, press
b
. The
program editor and program editor menu are displayed.
The program name is displayed at the top of the screen.
The cursor is on the first command line, which begins with
a colon. The TI
-
86 automatically places a colon at the
beginning of each command line.
As you write the program, the commands are stored to the program name.
The Program Editor Menu
8
'
programName
b
PAGE
$
PAGE
#
I
à
O CTL INSc
4
DELc UNDEL :
page down input
à
output insert a blank undelete (paste) a
menu command line deleted command line
page up program delete (cut) a paste a
control menu command line colon
The PRGM I
à
O (Input
à
Output) Menu
8
'
programName
b
(
PAGE
$
PAGE
#
I
à
O CTL INSc
Input Promp Disp DispG DispT
4
ClTbl Get Send getKy ClLCD
4
" Outpt InpSt
To see examples that show how to use
PRGM
I
à
O
menu items in programs, refer to the A to
Z Reference.
The
PRGM I
à
O
menu items
are instructions. The actions
they perform occur as the
program runs.
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Input
Displays the current graph and lets you use the free-moving cursor
Input
variable
Pauses a program, displays
?
as a prompt, and then stores your
response to
variable
Input
promptString
,variable
Input "string",variable
Pauses a program, displays
promptString
or
string
(up to 21
characters) as a prompt, and then stores your response to
variable
Input "CBLGET",variable
Although using
Get(
is preferred on the TI
-
86, you can use
Input
to
receive
variable
from a CBL 2/CBL, CBR, or TI
-
86 (TI
-
85 compatible)
Prompt variableA
ã
,variableB,variableC,...ä
Displays each
variable
with
?
to prompt you to enter a value for that
variable
Disp
Displays the home screen
Disp valueA,valueB,...
Displays each
value
Disp variableA,variableB,...
Displays the value stored to each
variable
Disp "textA","textB",...
Displays each
text
string on the left side of the current display line
DispG
Displays the current graph
DispT
Displays the current table and temporarily halts the program
ClTbl
Clears the current table if
Indpnt: Ask
is set (Chapter 7)
Get(variable)
Gets data from a CBL 2/CBL, CBR, or another TI
-
86 and stores it to
variable
Send(listName)
Sends the contents of
listName
to a CBL 2/CBL or CBR
getKy
Returns a number corresponding to the last key pressed, according
to the key code diagram (page 217); if no key was pressed, returns
0
ClLCD
Clears the home screen (LCD stands for liquid crystal display)
If you enter an expression for
variable
at an
Input
or
Prompt
prompt, it is
evaluated and stored.
For
Input
and
Prompt
, built-in
variables such as
y1
and
r1
are not valid as
variable
.
To halt the program
temporarily after
Disp
or
DispG
and examine what the
program is displaying, enter
Pause
on the next command
line (page 219).
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217
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"string"
Specifies the beginning and end of a
string
Outpt(row,column,"string")
Outpt(
row,column,stringName)
Outpt(
row,column,value)
Outpt(
row,column,variable)
Displays
string
,
stringName
,
value
, or a value stored to
variable
beginning at the specified
row
and
column
on the display
Outpt("CBLSEND",listName)
Although using
Send(
is preferred on the TI
-
86, you can use
Outpt(
to
send
listName
to a CBL 2/CBL or CBR (for TI
-
85 compatibility)
InpSt promptString,variable
InpSt variable
Pauses a program, displays
promptString
or
?
, and waits for a
response; stores the response to
variable
always as a string; omit
quotation marks from your response
The TI
-
86 Key Code Diagram
When
getKy
is encountered in a program, it returns a number
corresponding to the last key pressed, according to the key code
diagram to the right. If no key has been pressed,
getKy
returns
0
.
Use
getKy
inside loops to transfer control, such as when you
create a video game.
This program returns the key code of each key you press.
:Float
:0
A
:Lbl TOP
:getKy
A
:If A>0
:Disp A
:Goto TOP
To break (interrupt) the program, press ^ and then press *.
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The PRGM CTL Menu
8
'
programName
b
)
PAGE
$
PAGE
#
I
à
O CTL INSc
If Then Else For End
4
While Repea Menu Lbl Goto
4
IS> DS< Pause Retur Stop
4
DelVa GrStl LCust
To see examples that show how to use
PRGM
CTL
menu items in programs, refer to the A to
Z Reference.
If
condition
If
condition
is false (evaluates to 0), the next program command is
skipped; if
condition
is true (evaluates to a nonzero value), the
program continues on to the next command
Then
Following
If
, executes a group of commands if
condition
is true
Else
Following
If
and
Then
, executes a group of commands if
condition
is false
For(
variable
,
begin
,
end
ã
,
stepä
)
Starting at
begin
, repeats a group of commands by an optional real
step
until
variable
>
end
; default
step
is 1
End
Identifies the end of a group of program commands;
For(
,
While
,
Repeat
, and
Else
groups must end with
End
;
Then
groups without an
associated
Else
instruction also must end with
End
While
condition
Repeats a group of commands while
condition
is true;
condition
is
tested when the
While
instruction is encountered; typically, the
expression that defines
condition
is a relational test (Chapter 3)
Repeat
condition
Repeats a group of commands until
condition
is true;
condition
is
If
,
While
, and
Repeat
instructions can be nested.
For(
loops can be nested.
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219
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tested when the
End
instruction is encountered
Menu(item#,"title1",
label1ã,item#,
"title2",label2,
...
ä
)
Sets up branching within a program as selected from menu keys &
through *; when encountered, displays the first of up to 3 menu
groups (up to 15
titles
); when you select a
title
, the program
branches to the
label
that the
title
represents;
item
# is an integer
1
and
15 that specifies
title
’s menu placement;
title
is a text string
from one to eight characters long (may be abbreviated in the menu)
Lbl label
Assigns a
label
to a program command; label can be one to eight
characters long, starting with a letter
Goto label
Transfers control to the program branch labeled with
label
IS>(variable,value)
Adds 1 to
variable
; if the answer is >
value
, the next command is
skipped; if the answer is
value
, the next command is executed;
variable
cannot be a built-in variable
DS<(variable,value)
Subtracts 1 from
variable
; if the answer is <
value
, the next
command is skipped; if the answer is
value
, the next command is
executed;
variable
cannot be a built-in variable
Pause
Halts the program so that you can examine results, including
displayed graphs and tables; to resume the program, press b
Pause value
Displays
value
on the home screen so that you can scroll large
values, such as lists, vectors, or matrices; to resume, press b
Return
Exits a subroutine (page 224) and returns to the calling program,
even if encountered within nested loops; within the main program,
stops the program and returns to the home screen (an implied
Return
exits each subroutine upon completion and returns to the calling
program)
Stop
Stops a program and returns to the home screen
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DelVar(variable)
Deletes from memory
variable
(except program names) and its contents
GrStl(function#,graphStyle#)
Specifies the graph style represented by
graphStyle
# for the function
represented by
function
#;
function
# is the number part of an
equation variable, such as the
5
in
y5
;
graphStyle
# is an integer
1
and
7, where
1
= » (line),
2
= ¼ (thick),
3
= ¾ (shade above),
4
= ¿
(shade below),
5
= À (path),
6
= Á (animate), and
7
= Â (dotted)
*LCust(item#,"title"
ã,item#,"title",...ä)
Loads (defines) the TI
-
86 custom menu, which is displayed when you
press 9; item# is an integer
1 and
15;
title
is a string with
one to eight characters (may be abbreviated in the menu)
Entering a Command Line
You can enter on a command line any instruction or expression that you could execute on the
home screen. In the program editor, each new command line begins with a colon. To enter
more than one instruction or expression on a single command line, separate each with a colon.
To move the cursor down to the next new command line, press
b
. You cannot move to
the next new command line by pressing
#
. However, you can return to existing command
lines to edit them by pressing
$
.
Menus and Screens in the Program Editor
TI
-
86 menus and screens may be altered when displayed in the program editor. Menu items
that are invalid for a program are omitted from menus. Menus that are not valid in a
program, such as the
LINK
menu or
MEM
menu, are not displayed at all.
When you select a setting from a screen such as the mode screen or graph format screen,
the setting you select is pasted to the cursor location on the command line.
A command line that is longe
r
than the screen is wide
automatically continues at th
e
beginning of the next line.
All
CATALOG
items are valid
in the program editor.
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221
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Variables to which you typically store values from an editor, such as the window variables,
become items on program-only menus, such as the
GRAPH
WIND
menu. When you select
them, they are pasted to the cursor location on the command line.
Running a Program
Paste the program name to the home screen. Either select it from the
PRGM
NAMES
menu
(
8
&
) or enter individual characters.
Press
b
. The program begins to run.
Each result updates the last-answer variable
Ans
(Chapter 1). The TI
-
86 reports errors as
the program runs. Commands executed during a program do not update the previous-entry
storage area
ENTRY
(Chapter 1).
The example program below is shown as it would appear on a TI
-
86 screen. The program:
Creates a table by evaluating a function, its first derivative, and its second derivative at
intervals in the graphing window
Displays the graph of the function and its derivatives in three different graph styles,
activates the trace cursor, and pauses to allow you to trace the function
To resume the program after
a pause, press
b
.
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PROGRAM:FUNCTABL
:Func:Fix 2:FnOff:PlO
ff
:y1=.6 x cos x
:ClLCD
:Eq4St(y1,STRING)
:Outpt(1,1,"y1=")
:Outpt(1,4,STRING)
:Outpt(8,1,"PRESS ENT
ER")
:Pause
:ClLCD
:y2=der1(y1,x,x)
:y3=der2(y1,x,x)
:DispT
:GrStl(1,1):GrStl(2,2
):GrStl(3,7)
:2
xRes
:ZTrig
:Trace
The name of the program
Set graphing and decimal modes (mode screen); turn off
functions (
GRAPH
VARS
menu) and plots (
STAT
PLOT
menu)
Define the function (assignment statement)
Clear the home screen (
PRGM
I
à
O
menu)
Convert
y1
into the string variable
STRING
(
STRNG
menu)
Display
y1=
at row 1, column 1 (
PRGM
I
à
O
menu)
Display value stored to
STRING
at row 1, col. 4 (
PRGM
I
à
O
menu)
Display
PRESS ENTER
at line 8, column 1 (
PRGM
I
à
O
menu)
Pause the program (
PRGM
CTL
menu)
Clear the home screen (
PRGM
I
à
O
menu)
Define
y2
as the first derivative of
y1
(
CALC
menu)
Define
y3
as the second derivative of
y1
(
CALC
menu)
Display the table (
PRGM
I
à
O
menu)
Set graph styles for
y1
,
y2
, and
y3
(
PRGM
CTL
menu)
Store
2
to the window variable
xRes
(
GRAPH WIND
menu)
Set the viewing window variables (
GRAPH
ZOOM
menu)
Display the graph, activate trace cursor, and pause (
GRAPH
menu)
Breaking (Interrupting) a Program
To break (interrupt) the program, press
^
. The
ERROR 06 BREAK
menu is displayed.
To display the program editor where the interruption occurred, select
GOTO
(
&
).
To return to the home screen, select
QUIT
(
*
).
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Working with Programs
Managing Memory and Deleting a Program
To check whether adequate memory is available for a program you want to enter or
download, display the Check RAM screen (
-
&
; Chapter 17). To increase available
memory, consider deleting selected items or data types from memory (Chapter 17).
Editing a Program
After you write a program, you can display it in the program editor and edit any command line.
Display the program editor (
8
'
). The
PRGM
NAMES
menu also is displayed.
Enter the name of the program you want to edit. Either select the name from the
PRGM
NAMES
menu or enter the individual characters.
Edit the program command lines.
Move the cursor to the appropriate location, and then delete, overwrite, or insert characters.
Press
:
to clear the entire command line, except for the leading colon, and then enter a
new program command.
Select program editor menu items
INSc
(
*
) and
DELc
(
/
&
) to insert and delete
command lines.
The program editor does not
display a
$
to indicate that
command lines continue
beyond the screen.
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Calling a Program from Another Program
On the TI
-
86, any stored program can be called from another program as a subroutine. In
the program editor, enter the subroutine program name on a command line by itself.
Press
8
to display the
PRGM
NAMES
menu, and then select the program name.
Use ALPHA keys and alpha keys to enter the program name’s individual characters.
When the program name is encountered as the calling program runs, the next command
executed is the first command in the subroutine. It returns to the next command in the
calling program when it encounters
Return
(or implied
Return
) at the end of a subroutine.
Calling program Input
à
Output
Subroutine
label
used with
Goto
and
Lbl
is local to the program where it is located.
label
in one program is not
recognized by another program. You cannot use
Goto
to branch to a
label
in another program.
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Copying a Program to Another Program Name
Display a new or existing program in the program editor.
Move the cursor to the command line on which you want to copy a program.
Display the
Rcl
prompt (- ).
Enter the name of the program you want to copy. Either select the name from the
PRGM
NAMES
menu or enter individual characters.
Press b. The contents of the recalled program name are inserted into the other program at
the cursor location.
Using and Deleting Variables within a Single Program
If you want to use variables within a program but do not
need them after the program is run, you can use
DelVar(
within the program to delete the variables from memory.
The program segment to the right uses the variables A and
B as counters and then deletes them from memory.
:3
B
:For (A,1,100,1)
:B+A
B
:End
:Disp A
:Disp B
:DelVar(A)
:DelVar(B)
Running an Assembly Language Program
An assembly language program is a program that runs much faster and has greater control
of the calculator than the regular programs described in this chapter. You can download
and run TI-created assembly language programs to add features to your TI
-
86 that are not
built in. For example, you can download the TI
-
83 finance or inferential statistics features
to use on your TI
-
86.
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TI assembly language programs and other programs are available on TI’s World Wide Web site:
http:
àà
www.ti.com
à
calc
When you download an assembly language program, it is stored among the other programs
as a
PRGM
NAMES
menu item. You can:
Transmit it using the TI
-
86 communication link (Chapter 18).
Delete it using the
MEM
DELETE:PRGM
screen (Chapter 17).
Call it from another program as a subroutine (page 224).
To run an
assemblyProgramName
, the syntax is:
Asm(
assemblyProgramName
)
If you write an assembly language program, use the two instructions below from the
CATALOG
.
AsmComp(
AsciiAssemblyPrgmName
,
HexAssemblyPrgmName
)
Compiles an assembly language program written in ASCII
and stores the hex version
AsmPrgm
Identifies an assembly language program; must be
entered as the first line of an assembly language program
Entering and Storing a String
A string is a sequence of characters that you enclose within quotation marks.
A string defines characters to be displayed in a program.
A string accepts input from the keyboard in a program.
To enter a string directly, the syntax is:
"
string
"
To concatenate (join together) two or more strings, use
\
. The syntax is:
"
stringA
"+"
stringB
"+"
stringC
"+
...
You do not use quotation
marks to enter a string name.
In concatenation, you can
substitute
stringName
for
any
"
string
"
.
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The STRNG (String) Menu
-
" sub lngth Eq
4
St St
4
Eq
"
string
"
Marks the start and end of
string
sub("
string
",
begin
,
length
)
sub(
stringName
,
begin
,
length
)
Returns a subset of
"
string
"
or
stringName,
starting at
begin
character place and
length
characters long
lngth
"
string
"
or
lngth
stringName
Returns the number of characters in
"
string
"
or
stringName
Eq
4
St(
equationVariable
,
stringName
)
Converts
equationVariable
contents to
stringName
St
4
Eq(
stringName
,
equationVariable
)
Converts
stringName
to
equationVariable
Creating a String
Display the
STRNG
menu. -
Enter the open quotation mark, then
the string
SOLVE & GRAPH
, and then
the close quotation mark.
& 1 1
ã
S
ä
ã
O
ä
ã
L
ä
ã
V
ä
ã
E
ä
¤
- Ÿ & ( ¤
ã
G
ä
ã
R
ä
ã
A
ä
ã
P
ä
ã
H
ä
- &
Store the string to the string variable
name
LABEL
.
1 X
ã
L
ä
ã
A
ä
ã
B
ä
ã
E
ä
ã
L
ä
b
"
also marks the start and
end of a formula to be
attached to a list; it is also an
item on the list editor menu
(Chapter 11).
Begin these steps on a blank
line on the home screen or in
the program editor.
To evaluate the contents of a
string, you must use
St
4
Eq(
to convert it to an equation.
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17MEMORY.DOC TI-86, Chap17, US English Bob Fedorisko Revised: 02/13/01 2:37 PM Printed: 02/13/01 3:05 PM Page 229 of 4
Checking Available Memory ............................................ 230
Deleting Items from Memory ...........................................231
Resetting the TI
-
86 .......................................................... 232
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
17
Memory Management
230
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Checking Available Memory
The MEM (Memory) Menu
-
RAM DELET RESET TOL ClrEnt
check-RAM memory/default clears ENTRY
screen reset menu storage area
memory delete tolerance
menu editor
Checking Memory Usage
-
&
When all memory is cleared and all defaults are set, the
standard TI
-
86 has
98,224
bytes of available random-access
memory (RAM). As you store information to RAM, you can
monitor memory allocation on the Check RAM screen.
MEM
FREE
reports the total number of bytes available in
RAM. Conversely, all other numbers on the screen report
the number of bytes that each data type currently occupies. For example, if you were to
store a 50-byte matrix in memory, the
MATR
total would increase to
50
bytes, while the
MEM
FREE
total would decrease by 50 to
98174
bytes.
To display the number of bytes that a specific variable occupies, display the
DELETE
screen
for that data type (page 231). Scroll the screen, if necessary.
For information on
TOL
(the
tolerance editor), refer to the
Appendix.
Chapter 17: Memory Management
231
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Deleting Items from Memory
The MEM DELET (Delete) Menu
-
'
ALL REAL CPLX LIST VECTR
4
MATRX STRNG EQU CONS PRGM
4
GDB PIC
Each
MEM
DELET
menu item displays the deletion screen for that data type. For example,
when you select
LIST
, the
MEM DELETE:LIST
screen is displayed. Use the
DELETE
screens to
delete any user-created variable and the information stored to it.
Select
DELET
from the
MEM
menu to
display the
MEM
DELET
menu.
Select the data type of the item you want
to delete. To scroll down to the next six
items or up to the previous six items,
select
PAGE
$
or
PAGE
#
.
-
'
/
(
Move the selection cursor (
4
) to the item
you want to delete (
y5
). The uppercase
items are in alphanumeric order, followed by
the lowercase items in alphanumeric order.
Delete the item. To delete other items on
the screen, repeat steps 3 and 4.
#
#
#
b
To delete a parametric
equation, delete the
xt
component.
In the example, the equation
y5=x^3
N
x
2
+4x
N
1
is deleted.
To move directly to the first
item beginning with any
letter, enter that letter;
ALPHA-lock is on.
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Resetting the TI-86
The MEM RESET (Reset) Menu
-
(
RAM DELET RESET TOL ClrEnt
ALL MEM DFLTS
ALL
When confirmed, all data is cleared and memory is reset; both messages are displayed
MEM
When confirmed, clears all stored data from memory;
Mem Cleared
is displayed
DFLTS
When confirmed, resets all defaults;
Defaults Set
is displayed
When you select
ALL
,
MEM
, or
DFLTS
, a confirmation menu
is displayed.
To confirm the selected reset, select
YES
(press
)
).
To cancel the selected reset, select
NO
(press
*
).
ClrEnt (Clear Entry)
-
*
The TI
-
86 retains as many previous entries as possible in
ENTRY
, up to a capacity of 128 bytes.
To clear the
ENTRY
storage area of all entries, execute
ClrEnt
on a blank line on the home screen (
-
*
b
).
Before resetting all memory,
consider deleting selected
information to increase
memory capacity (page 231).
When you select and confirm
ALL
or
DFLTS
, the default
contrast is reset; to adjust it,
use
-
$
or
-
#
(Chapter 1).
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TI
-
86 Linking Options ...................................................... 234
Connecting the TI
-
86 to Another Device .........................235
Selecting Data to Send..................................................... 236
Preparing the Receiving Device ....................................... 240
Transmitting Data............................................................240
Receiving Transmitted Data............................................. 240
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
18
The TI-86
Communication Link
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-
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TI-86 Linking Options
Using the unit-to-unit cable included with the TI
-
86, you can transmit data between the
TI
-
86 and several other devices.
Linking Two TI-86s
You can link two TI
-
86 units and select the data types to be transmitted, including
programs. You can back up the entire memory of a TI
-
86 onto another TI
-
86.
Linking a TI-86 and a TI-85
You can select the data types, including programs, to transfer from a TI
-
85 to a TI
-
86. You
can send most variables and programs from a TI
-
86 to a TI
-
85 using
SND85
(page 239),
except lists, vectors, or matrices that exceed TI
-
85 capacity.
When you run a TI
-
85 program on a TI
-
86, the TI
-
85
PrtScrn
program instruction is not
valid. Also, the EOS implied multiplication on the TI
-
86 differs from the TI
-
85 (Appendix).
For example, the TI
-
85 interprets
sin 2x
as
sin (2x)
; the TI
-
86 interprets
sin 2x
as
(sin 2)x
.
Linking a TI-86 and a CBL 2/CBL or CBR System
The Calculator-Based Laboratory
é
(CBL 2
é
/CBL
é
) and Calculator-Based Ranger
é
(CBR
é
) systems are optional TI accessories that collect data from physical occurrences,
such as science experiments. The CBL 2/CBL and CBR store data to lists, which you can
transmit to a TI
-
86 and analyze. You can transmit list names to a CBL 2/CBL or CBR from a
TI
-
86.
Chapter 18: The TI
-
86 Communication Link
235
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Linking a TI-86 and a PC or Macintosh
TI
-
86 TI-GRAPH LINK
è
is an optional system that links a TI
-
86 with an IBM
ê
-compatible or
Macintosh
ê
computer.
Downloading Programs from the Internet
If you have
TI-GRAPH LINK
and internet services, you can download programs from TI’s
World Wide Web site at:
http:
àà
www.ti.com
à
calc
You can download various programs from TI’s web site, including assembly language programs
that add features such as TI
-
83 finance and inferential statistics. The site also links to many
other TI
-
86 web sites maintained by user groups, high schools, universities, and individuals.
Connecting the TI-86 to Another Device
Before you begin to transmit data to or from the TI
-
86, connect it to the other device.
Firmly insert one end of the unit-to-unit cable into the port on the bottom edge of the calculator.
Firmly insert the other end of the cable into the other device (or PC adapter).
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-
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The LINK Menu
-
o
SEND RECV SND85
menu of data menu of data types
types to send to send to a TI
-
85
receive mode
(waiting)
Selecting Data to Send
To list the variables for a specific data type on a selection screen, select the data type from
the
LINK
SEND
menu. When you select
BCKUP
, the message
Memory Backup
is displayed.
The LINK SEND Menu
-
o
&
memory all real and complex values in
backup matrices complex data types vectors all data types
graph real values in
programs databases lists all data types equations
BCKUP PRGM MATRX GDB ALL
4
LIST VECTR REAL CPLX EQU
4
CONS PIC WIND STRNG
user-created window
constants variable
pictures values strings
The link menus are not
available in the program
editor.
The CBL 2/CBL, CBR, and
TI
-
86
TI-GRAPH LINK
have
built-in Silent Link, which
eliminates the need for you to
set up the devices to send or
receive.
Chapter 18: The TI
-
86 Communication Link
237
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Initiating a Memory Backup
To initiate a memory backup, select
BCKUP
from the
LINK
SEND
menu (
-
o
&
&
). The screen to the right is
displayed.
To complete memory backup, prepare the other unit to
receive data transmission (page 239), and then select
XMIT
from the memory backup menu (
&
).
Warning:
When you transmit
BCKUP
, the transmitted memory overwrites all memory in
the receiving unit; all information in the memory of the receiving unit is lost. To cancel
initiation of a memory backup, press
.
.
As a safety check to prevent accidental loss of memory,
when the receiving calculator is notified of an incoming
backup transmission, it displays the warning message and
confirmation menu, as shown in the screen to the right.
To continue the backup transmission, select
CONT
.
The backup transmission continues, replacing all
receiving-calculator memory with the backup data.
To cancel backup and retain all receiving-calculator memory, select
EXIT
.
Selecting Variables to Send
If a transmission error occurs
during a backup, the
receiving-calculator memory
is reset.
If no data of the type you
select is stored in memory,
the message is displayed:
NO VARS OF THIS TYPE
.
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-
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When you select any
LINK
SEND
menu item, except
BCKUP
or
WIND
, each variable of the selected data type is listed in
alphanumeric order on a selection screen. The screen to
the right is the
SEND
ALL
screen (
-
o
&
*
).
The data type of each variable is specified.
Small squares indicate that
xStat
,
yStat
, and
Q2
are
selected to be sent.
The selection cursor is next to
Q4
.
To select a specific variable to be sent, use
#
and
$
to move the selection cursor next to
the variable, and then select
SELCT
(
'
) from the selection screen menu.
To select all variables of this type, select
ALL+
from the selection screen menu (
(
).
To deselect all variables of this type, select
ALL-
from the selection screen menu (
)
).
To complete transmission of the selected variables, prepare the other unit to receive data
transmission (page 239), and then select
XMIT
from the selection screen menu (
&
).
The SEND WIND (Window Variables) Screen
When you select
WIND
from the
LINK
SEND
menu (
-
o
&
/
/
(
), the
SEND
WIND
screen is displayed.
Each
SEND
WIND
screen item represents the window
variables, format settings, and any other graph-screen data
for that TI
-
86 graphing mode and for
ZRCL
(user-created
zoom). The screen to the right shows that the graph screen
data for
Func
and
DifEq
graphing modes are selected.
Func
Select to send
Func
graphing mode window variable values and format settings
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-
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239
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Pol
Select to send
Pol
graphing mode window variable values and format settings
Param
Select to send
Param
graphing mode window variable values and format settings
DifEq
Select to send
DifEq
graphing mode window variable values,
difTol
, axes settings, and
format settings
ZRCL
Select to send user-created zoom window variables, and format settings in any mode
To complete transmission of the selected variables, prepare the other unit to receive data
transmission (below), and then select
XMIT
from the memory backup menu (
&
).
Sending Variables to a TI-85
The steps for selecting variables to send to a TI
-
85 are the same as those for selecting variables
to send to a TI
-
86. However, the
LINK
SND85
menu has fewer items than the
LINK
SEND
menu.
The TI
-
86 has more capacity for lists, vectors, and matrices than the TI
-
85. If you send to the
TI
-
85 a list, vector, or matrix that has more elements than the TI
-
85 allows, the elements that
exceed TI
-
85 capacity are truncated.
The LINK SND85 (Send Data to TI-85) Menu
-
o
(
MATRX LIST VECTR REAL CPLX
4
CONS PIC STRNG
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-
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Preparing the Receiving Device
To prepare a TI
-
86 or TI
-
85 to receive data transmission,
select
RECV
from the
LINK
menu (
-
o
'
). The
message
Waiting
and the busy indicator are displayed. The
calculator is ready to receive transmitted items.
To cancel receive mode without receiving items, press
^
. When the
LINK TRANSMISSION
ERROR
message is displayed, select
EXIT
from the menu (
&
). The
LINK
menu is displayed.
Transmitting Data
After you select data types on the sending unit and prepare the receiving unit to receive
data, you can begin transmitting.
To begin transmitting, select
XMIT
on the selection screen menu of the sending calculator (
&
).
To interrupt transmission, press
^
on either calculator. When the
LINK TRANSMISSION
ERROR
message is displayed, select
EXIT
from the menu (
&
). The
LINK
menu is displayed.
Receiving Transmitted Data
As the TI
-
86 receives transmitted data, each variable name and data type is displayed line
by line. If all selected items are transmitted successfully, the message
Done
is displayed. To
scroll the transmitted variables, press
#
and
$
.
To prepare a PC to receive
data, consult the
TI-GRAPH
LINK
guidebook.
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-
86 Communication Link
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During transmission, if a transmitted variable name is
stored already in the memory of the receiving calculator,
transmission is interrupted. The duplicated variable name,
its data type, and the
DUPLICATE
NAME
menu are
displayed, as shown in the screen to the right.
To resume or cancel transmission, you must select an item
from the
DUPLICATE
NAME
menu.
RENAM
Displays the
Name=
prompt; enter a unique variable name; press
b
to continue
transmission
OVERW
(overwrite) Replaces data stored to the receiving unit’s variable with sent variable data
SKIP
Does not overwrite the receiving unit’s data; attempts to send the next selected variable
EXIT
Cancels the data transmission
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Repeating Transmission to Several Devices
After transmission is complete, the
LINK
menu is displayed and all selections remain. You can
transmit the same selections to a different TI
-
86 without having to re-select data.
To repeat a transmission with another device, disconnect the unit-to-unit cable from the
receiving unit; connect it to another device; prepare the device to receive data; and then
select
SEND
, then
ALL
, and then
XMIT
.
Error Conditions
A transmission error occurs after a few seconds if:
The cable is not connected to the port of the sending calculator.
The cable is not connected to the port of the receiving calculator.
The receiving unit is not set to receive transmission.
You attempt a backup between a TI
-
86 and a TI
-
85.
Insufficient Memory in Receiving Unit
If the receiving unit does not have sufficient memory to receive an item, the receiving unit
displays
LINK MEMORY FULL
and the variable name and data type.
To skip the variable, select
SKIP
. Transmission resumes with the next item.
To cancel transmission altogether, select
EXIT
.
If the cable is connected but
a transmission error occurs,
push the cable in more firmly
to both calculators and try
again.
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Using Math Operations with Matrices.............................244
Finding the Area between Curves.................................... 245
The Fundamental Theorem of Calculus............................ 246
Electrical Circuits.............................................................. 248
Program: Taylor Series .....................................................250
Characteristic Polynomial and Eigenvalues...................... 252
Convergence of the Power Series .................................... 254
Reservoir Problem............................................................ 256
Predator-Prey Model........................................................ 258
Program: Sierpinski Triangle ............................................ 260
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
19
Applications
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Using Math Operations with Matrices
In the matrix editor, enter matrix
A
as shown.
On the home screen, select
rref
from the
MATRX
OPS
menu.
To append a 3×3 identity matrix to matrix
A
, select
aug
from the
MATRX
OPS
menu, enter
A
, select
ident
from the
MATRX
OPS
menu, and then enter
3
. Execute the expression.
Enter
Ans
(to which the matrix from step 3 is stored). Define a
submatrix that contains the solution portion of the result. The
submatrix begins at element (1,4) and ends at element (3,6).
Select
4
Frac
from the
MATH
MISC
menu and display the
fractional equivalent of the submatrix.
Check the result. Set the decimal mode to 11 (the last
1
) Select
round
from the
MATH
NUM
menu for the product of the
fractional equivalent of the submatrix times
A
.
Displaying the result matrix
elements to 11 decimal
places illustrates accuracy.
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Finding the Area between Curves
Find the area of the region bounded by: f(x)=300 x
à
(x
2
+625)
g(x)=3 cos (.1 x)
x=75
In
Func
graphing mode, select
y(x)=
from the
GRAPH
menu to display the equation editor and
enter the equations as shown.
y1=300 x
à
(x
2
+625) y2=3 cos (.1 x)
Select
WIND
from the
GRAPH
menu and set the window variables as shown.
xMin=0 xMax=100 xScl=10 yMin=
L
5 yMax=10 yScl=1 xRes=1
Select
GRAPH
from the
GRAPH
menu to display the graph screen.
Select
ISECT
from the
GRAPH MATH
menu. Move the trace cursor to the intersection of the
functions. Press
b
to select
y1
. The cursor moves to
y2
. Press
b
. Then press
b
again to set the current cursor location as the initial guess. The solution uses the solver. The
value of
x
at the intersection, which is the lower limit of the integral, is stored to
Ans
and
x
.
The area to integrate is between
y1
and
y2
, from
x=5.5689088189
to
x=75
. To see the area on a graph, return to the home screen,
select
Shade
from the
GRAPH
DRAW
menu, and execute this
expression:
Shade(y2,y1,Ans,75)
Select
TOL
from the
MEM
menu and set
tol=1
E
L
5
.
On the home screen, compute the integral with
fnInt
(
CALC
menu). The area is 325.839961998.
fnInt(y1
N
y2,x,Ans,75)
If necessary, select
ALL-
from the equation editor
menu to deselect all
functions. Also, turn off all
stat plots.
246
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The Fundamental Theorem of Calculus
Consider these three functions:
F(x)
1
= (sin x)
à
x F(x)
2
=
0
x
(sin t)
à
tF(x)
3
=
d
dx
0
x
(sin t)
à
t dt
In
Func
graphing mode, select
y(x)=
from the
GRAPH
menu, and then enter the functions and set
graph styles in the equation editor as shown. (
fnInt
and
nDer
are
CALC
menu items.)
Ây1=(sin x)
à
x »y2=fnInt(y1(t),t,0,x) ¼y3=nDer(y2,x)
Select
TOL
from the
MEM
menu to display the tolerance editor. To improve the rate of the
calculations, set
tol=0.1
and
d
=0.001
.
Select
WIND
from the
GRAPH
menu and set the window variable values as shown.
xMin=
L
10 xMax=10 xScl=1 yMin=
L
2.5 yMax=2.5 yScl=1 xRes=4
Select
TRACE
from the
GRAPH
menu to display the graph and
the trace cursor.
Trace
y1
and
y3
to verify that the graph of
y1
and the graph of
y3
are visually indistinguishable.
The inability to visually distinguish between the graphs of
y1
and
y3
graphically supports the fact that:
d
dx
0
x
(sin t)
à
t dt = (sin x)
à
x
If necessary, select
ALL-
from the equation editor
menu to deselect all
functions. Also, turn off all
stat plots.
In the example,
nDer(y2,x)
only approximates
y3
; you
cannot define
y3
as
der1(y2,x)
.
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Deselect
y2
in the equation editor.
Select
TBLST
from the
TABLE
menu. Set
TblStart=1
,
@
Tbl=1
, and
Indpnt: Auto
.
Select
TABLE
from the
TABLE
menu to display the table.
Compare the solution of
y1
with the solution of
y3
to numerically
support the formula above.
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Electrical Circuits
A measurement device has measured the DC current (C) in milliamperes and voltage (V) in
volts on an unknown circuit. From these measurements, you can calculate power (P) in
milliwatts using the equation
CV=P
. What is the average of the measured power?
With the TI
-
86, you can estimate the power in milliwatts at a current of 125 milliamperes
using the trace cursor, the interpolate
à
extrapolate editor, and a regression forecast.
In two consecutive columns of the list editor, store the current
measurements shown below to the list name
CURR
and the
voltage measurements shown below to the list name
VOLT
.
{10,20,40,60,80,100,120,140,160}
CURR
{2,4.2,10,18,32.8,56,73.2,98,136}
VOLT
In the next column of the list editor, enter the list name
POWER
.
Enter the formula
CURR
¹
VOLT
in the list editor entry line for
POWER
. Press
b
to calculate the values for power and store
the answers to the list name
POWER
.
Select
WIND
from the
GRAPH
menu and set the window variable values as shown.
xMin=0 xMax=max(POWER) xScl=1000 yMin= 0 yMax=max(CURR) yScl=10 xRes=4
From the home screen, select
FnOff
from the
CATALOG
and
press
b
to deselect all functions in the equation editor.
Select
Plot1(
from the
CATALOG
and set up a stat plot with
POWER
on the x-axis and
CURR
on the y-axis.
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Select
TRACE
from the
GRAPH
menu to display the stat plot and
trace cursor on the graph screen.
Trace the stat plot to approximate the value of
POWER
at
CURR=125
. With this statistical data, the closest to
CURR=125
that you can trace to is
CURR=120
(on the y-axis).
Select
INTER
from the
MATH
menu to display the
interpolate
à
extrapolate editor. To interpolate
POWER
at
CURR=125
, enter the nearest pairs:
x1=POWER(7) y1=CURR(7)
x2=POWER(8) y2=CURR(8)
Enter
y=125
and solve for
x
.
µ
On the home screen, select
LinR
from the
STAT
CALC
menu to fit
the linear regression model equation to the data stored to
POWER
and
CURR
. Write down the value of the result variable
corr
.
¸
Fit the logarithmic (
LnR
), exponential (
ExpR
), and power (
PwrR
) regressions to the data, writing
down the value of
corr
for each regression. Compare the
corr
values of each regression to
determine which model fits the data most accurately (the
corr
value closest to
1
).
¹
Execute the most accurate regression again, and then select
FCST
from the
STAT
menu. To forecast
POWER
at
CURR=125
,
enter
y=125
and solve for
x
.
Compare this answer with the answer returned in step 9.
The
7
s and
8
s in parentheses
specify the 7th and 8th
elements of
POWER
and
CURR
.
To enter each regression
after
LinR
, press
-
¢
and edit as needed.
250
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Program: Taylor Series
When you run this program, you can enter a function and specify the order and center
point. Then the program calculates the Taylor Series approximation for the function and
plots the function you entered. This example shows how to call a program from another
program as a subroutine.
Before you enter the program
TAYLOR
, select
EDIT
from the
PRGM
menu, enter
MOBIUS
at the
Name=
prompt, and then enter this brief program to store the Mobius Series. The program
TAYLOR
calls this program and runs it as a subroutine.
PROGRAM:MOBIUS
:{1,
L
1,
L
1,0,
L
1,1,
L
1,0,0,1,
L
1,0,
L
1,1,1,0,
L
1,0,
L
1,0}
MSERIES
:Return
Select
EDIT
from the
PRGM
menu, enter
TAYLOR
at the
Name=
prompt, and then enter this
program to calculate the Taylor Series.
PROGRAM:TAYLOR
:Func:FnOff
:y14=pEval(TPOLY,x
N
center)
:GrStl(14,2)
H
is on the
CHAR GREEK
menu
:1
E
L
9
H
:.1
rr
:ClLCD
User enters equation function
:InpSt "FUNCTION: ",EQ
:St
8
Eq(EQ,y13)
User enters order
:Input "ORDER: ",order
:order+1
dimL TPOLY
:Fill(0,TPOLY)
User enters center
:Input "CENTER: ",center
:evalF(y13,x,center)
f0
:f0
TPOLY(order+1)
The higher-order derivative
values necessary for this
program are calculated
numerically based on the
methods in “Numerical
Differentiation of Analytic
Functions,” J. N. Lyness and
C. B. Moler, SIAM Journal of
Numerical Analysis 4 (1967):
202-210.
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:If order
1
:der1(y13,x,center)
TPOLY(order)
:If order
2
:der2(y13,x,center)
à
2
TPOLY(order
N
1)
:If order
3
Begins
Then
group
:Then
Calls subroutine
:MOBIUS
Begins
For
group
:For(N,3,order,1)
:abs f0
gmax:gmax
bmi
:1
m:0
ssum
Begins
While
group
:While abs bmi
‚H
¹
gmax
:While MSERIES(m)==0
Creates nested
While
group
:m+1
m
:End
:0
bsum
:For(J,1,m
¹
N,1)
:rr
¹
e^(2
p
(J
à
(m
¹
N))
¹
(0,1))+(center,0)
x
Creates nested
For
group
:real y13
gval
:bsum+gval
bsum
:max(abs gval,gmax)
gmax
:End
:bsum
à
(m
¹
N)
N
f0
bmi
:ssum+MSERIES(m)
¹
bmi
ssum
:m+1
m
Ends
While
group
:End
:ssum
à
(rr^N)
TPOLY(order+1
N
N)
Ends
For
group
:End
Ends
Then
group
:End
:ZStd
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On the home screen, select
TAYLOR
from the
PRGM
NAMES
menu, and then press b to run the program.
When prompted, enter:
FUNCTION: sin x
ORDER: 5
CENTER: 0
Characteristic Polynomial and Eigenvalues
In the matrix editor or on the home screen, enter matrix
A
as shown.
[[
L
1,2,5][3,
L
6,9][2,
L
5,7]]
A
On the home screen, select
eigVl
from the
MATRX
MATH
menu
to find the complex eigenvalues for the matrix
A
and store them
to the list name
EV
.
Graph the characteristic polynomial Cp(x) of matrix
A
without knowing the analytic form of
Cp(x) based on the formula Cp(x)=det(A
N
x¹I). In
Func
graphing mode, select
y(x)=
from the
GRAPH
menu and enter the function in the equation editor as shown.
»
y1=det (A
N
x
¹
ident 3)
Select
WIND
from the
GRAPH
menu and set the window variable values as shown.
xMin=
L
10 xMax=10 xScl=1 yMin=
L
100 yMax=50 yScl=10 xRes=4
Select
ROOT
from the
GRAPH
MATH
menu and use it to display
the real eigenvalue interactively. Use
Left Bound=
L
5
,
Right Bound=
L
4
, and
Guess=
L
4.5
.
Compare the root (
x
value) you displayed interactively with the
first element of the result list in step 2.
The first eigenvalue is real,
since the imaginary part is
0
.
If necessary, select
ALL-
from the equation editor
menu to deselect all
functions. Also, turn off all
stat plots.
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Next, use the list editor and a degree-three polynomial regression to find an analytic formula in
terms of
x
for the characteristic polynomial
y1=det(A
N
x¹ident 3)
. Create two lists that you can
use to find the analytic formula.
In the list editor, create elements for
xStat
by entering the
expression
seq(N,N,
L
10,21)
in the
xStat
entry line.
seq
is on the
MATH
MISC
menu.
Create elements for
yStat
by attaching the formula
"y1(xStat)"
to
yStat
in the entry line. The expression is evaluated when you
press b or exit the list editor.
On the home screen, select
Plot1(
from the
CATALOG
and
execute
Plot1(2,xStat,yStat,1)
to turn on
Plot1
as an xyLine plot
using the lists
xStat
and
yStat
.
Select
GRAPH
from the
GRAPH
menu to display
Plot1
and
y1
on
the graph screen.
µ
On the home screen, select
P3Reg
from the
STAT
CALC
menu.
Execute
P3Reg xStat,yStat,y2
to find the explicit characteristic
polynomial in terms of
x
and store it to
y2
.
The cubic regression coefficients stored in the result list
PRegC
suggest that a=
L
1, b=0, c=14, and d=
L
24. So the characteristic
polynomial seems to be Cp(x)=
L
x
3
+14x
N
24.
To clear the menus from the
graph screen, press
:
.
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¸
Support this conjecture by graphing
y1
,
y2
(to which Cp(x) is
stored), and
Plot1
together.
¹
In the equation editor, enter the apparent characteristic
polynomial of matrix
A
and select ¼ (thick) graph style as shown.
¼y3=
L
x^3+14x
N
24
Ƹ
Graph
y1
,
y2
,
y3
, and
Plot1
.
ƹ
Deselect
y2
in the equation editor.
ƺ
Select
TABLE
from the
TABLE
menu to display
y1
and
y3
in the
table.
Compare the values for the characteristic polynomial.
Convergence of the Power Series
A closed-form analytic antiderivative of (sin x)
à
x does not exist. However, substituting t for
x, you can find an infinite series analytic solution by taking the series definition of sin t,
dividing each term of the series by t, and then integrating term by term to yield:
ˆ
G
L
1
n+1
t
2n
N
1
à
((2n
N
1)(2n
N
1)!)
n=1
Plot finite approximations of this power series solution on the TI
-
86 with
sum
and
seq
.
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Select
TOL
from the
MEM
menu and set
tol=1
.
On the mode screen, set
Radian
angle mode and
Param
graphing mode.
In the equation editor, enter the parametric equations for the power series approximation as
shown. Select
sum
and
seq
from the
LIST
OPS
menu. Select
!
from the
MATH
PROB
menu.
»xt1=t yt1=sum seq((
L
1)^(j+1)t^(2j
N
1)
à
((2j
N
1)(2j
N
1)!),j,1,10,1)
In the equation editor, enter the parametric equations as shown to plot the antiderivative of (sin x)
à
x
and compare it with the plot of the power series approximation. (Select
fnInt
from the
CALC
menu.)
¼xt2=t yt2=fnInt((sin w)
à
w,w,0,t)
Select
WIND
from the
GRAPH
menu and set the window variable values as shown.
tMin=
L
15 xMin=
L
15 yMin=
L
3
tMax=15 xMax=15 yMax=3
tStep=0.5 xScl=1 yScl=1
Select
FORMT
from the
GRAPH
menu and set
SimulG
format.
Select
GRAPH
from the
GRAPH
menu to plot the parametric
equations on the graph screen.
In the equation editor, modify
yt1
to compute the first 16 terms of
the power series by changing
10
to
16
. Plot the equations again.
In this example, the window variable
tStep
controls the plotting
speed. Select
WIND
from the
GRAPH
menu and set
tStep=1
and
observe the difference in plotting speed and curve smoothness.
If necessary, select
ALL
N
from the equation editor
menu to deselect all
functions. Also, turn off all
stat plots.
This example is set up in
Param
mode, which allows
you to control the solution
with
tStep
and increase
plotting speed.
To clear the menus from the
graph screen, press
:
.
256
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Reservoir Problem
On the TI
-
86, you can use parametric graphing animation to solve a problem.
Consider a water reservoir with a height of 2 meters. You must install a small valve on the
side of the reservoir such that water spraying from the open valve hits the ground as far
away from the reservoir as possible. At what height should you install the valve to
maximize the length of the water stream when the valve is wide open?
Assume a full tank at time=0, no acceleration in the x direction, and no initial velocity in the
y direction. Also, ignore valve-size and valve-type factors. Integrating the definition of
acceleration in both the x and y directions twice yields the equations x=v
0
t and
y=h
0
N
(gt
2
)
à
2. Solving Bernoulli’s equation for v
0
and substituting into v
0
t results in this pair
of parametric equations:
xt=t
(2g(2
N
h
0
)) yt=h
0
N
(gt
2
)
à
2
t = time in seconds
h
0
= height of the valve in meters
g = the built-in acceleration of gravity constant
When you graph these equations on the TI
-
86, the y-axis (x=0) is the side of the reservoir
where the valve is to be installed. The x-axis (y=0) is the ground. Each plotted parametric
equation represents the water stream when the valve is at each of several heights.
Chapter 19: Applications
257
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In
Param
graphing mode, select
E(t)=
from the
GRAPH
menu and enter the equations in the
equation editor as shown. This pair of equations plots the path of the water stream when the
valve is installed at a height of 0.5 meters.
»xt1=t
(2g(2
N
0.5)) yt1=0.5
N
(g¹t
2
)
à
2
Move the cursor to
xt2=.
Press - ' 1
1
, and press b to recall the contents of
xt1
into
xt2
. For
xt2
, change the valve height (which is
0.5
) to
0.75
meters. Do the same with
yt1
and
yt2
.
Repeat step 3 to create three more pairs of equations. Change the valve height to
1.0
meters for
xt3
and
yt3
,
1.5
meters for
xt4
and
yt4
, and
1.75
meters for
xt5
and
yt5
.
Select
WIND
from the
GRAPH
menu and set the window variable values as shown.
tMin=0 xMin=0 yMin=0
tMax=
(4
à
g) xMax=2 yMax=2
tStep=0.01 xScl=0.5 yScl=0.5
Select
FORMT
from the
GRAPH
menu and set
SimulG
graph
format.
Select
GRAPH
from the
GRAPH
menu to plot the trajectory of
the water jets from the five specified heights.
Which height seems to create the longest water stream?
If necessary, select
ALL
N
from the equation editor
menu to deselect all
functions. Also, turn off all
stat plots.
To clear the menus from the
graph screen, press
:
.
258
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Predator-Prey Model
The growth rates of predator and prey populations, such as foxes and rabbits, depend upon the
populations of both species. This initial-value problem is a form of the predator-prey model.
F'=
L
F+0.1F
¹
R R'=3R
N
F
¹
R
Q1
= population of foxes (F)
Q2
= population of rabbits (R)
Q
[
1
= initial population of foxes (2)
Q
[
2
= initial population of rabbits (5)
Find the population of foxes and rabbits after 3 months (
t=3
).
In
DifEq
graphing mode, select
Q't=
from the
GRAPH
menu and enter the functions and set graph
styles in the equation editor as shown.
¼Q'1=
L
Q1+0.1Q1¹Q2 »Q'2=3Q2
N
Q1¹Q2
Select
FORMT
from the
GRAPH
menu and set
FldOff
field format.
Select
WIND
from the
GRAPH
menu and set the window variable values as shown.
tMin=0 xMin=
L
1 yMin=
L
10
tMax=10 xMax=10 yMax=40
tStep=
24 xScl=5 yScl=5
tPlot=0 difTol=.001
Select
INITC
from the
GRAPH
menu and set the initial conditions as shown.
tMin=0 Q
[
1=2 Q
[
2=5
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259
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Select
GRAPH
from the
GRAPH
menu to plot the graph of the
two populations over time.
To see the direction field of the phase-plane solution, select
FORMT
from the
GRAPH
screen, and then set
DirFld
field
format.
Select
INITC
from the
GRAPH
menu and delete the values for
Q
[
1
and
Q
[
2
.
Select
GRAPH
from the
GRAPH
menu to display the direction
field of the phase-plane solution.
To see a family of specific phase-plane solutions on top of the
direction field, select
INITC
from the
GRAPH
menu, and then
enter lists for
Q
[
1
and
Q
[
2
as shown.
Q
[
1={2,6,7} Q
[
2={6,12,18}
µ
Select
TRACE
from the
GRAPH
menu to display the graph with
the trace cursor.
¸
Press
3
to see how many foxes and how many rabbits are alive at
t=3
. (Round the values of
Q1
(foxes) and
Q2
(rabbits) to whole
numbers.) How many foxes and rabbits are alive at
t=6
? at
t=12
?
On what value of
Q1
and
Q2
do the phase-plane orbits seem to
converge? What is the significance of this value?
260
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Program: Sierpinski Triangle
This program creates a drawing of a widely known fractal, the Sierpinski Triangle, and
stores the drawing to the picture variable
TRI
.
Select
EDIT
from the
PRGM
menu, enter
SIERP
at the
Name=
prompt, and then enter this program.
PROGRAM:SIERP
:FnOff :ClDrw
:PlOff
:AxesOff
Sets viewing
window
:0
xMin:1
xMax
:0
yMin:1
yMax
:rand
X:rand
Y
Begins
For
group
:For(K,1,3000)
:rand
N
If
à
Then
group
:If N
(1
à
3)
:Then
:.5X
X
:.5Y
Y
:End
If
à
Then
group
:If N>(1
à
3) and N
(2
à
3)
:Then
:.5(.5+X)
X
:.5(1+Y)
Y
:End
If
à
Then
group
:If N>(2
à
3)
:Then
:.5(1+X)
X
:.5Y
Y
:End
Draws point
:PtOn(X,Y)
End of
For
:End
Stores picture
:StPic TRI
On the home screen, select
SIERP
from the
PRGM
NAMES
menu
and press
b
to run the program, which may run for several
minutes before completion.
After you run the program, you can recall and display the picture
by executing
RcPic TRI
.
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Quick-Find Locator........................................................... 262
Alphabetical Listing of Operations................................... 266
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
A to Z Function and
Instruction Reference
20
262
Chapter 20: A to Z Function and Instruction Reference
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Quick-Find Locator
This section lists the TI
-
86 functions and instructions in functional groups along with the page numbers where they are
described in this chapter.
Graphing
Axes(
...................271
AxesOff
...............271
AxesOn
................271
Circl(
....................273
ClDrw
...................273
CoordOff
.............275
CoordOn
..............275
DifEq
....................281
DirFld
...................282
DrawDot
..............285
DrawF
..................286
DrawLine
.............286
DrEqu(
.................287
DrInv
....................287
dxDer1
.................288
dxNDer
.................288
FldOff
...................295
FnOff
....................296
FnOn
....................297
Func
.....................299
GridOff
.................301
GridOn
.................302
GrStl(
...................302
Horiz
....................304
LabelOff
...............310
LabelOn
...............310
Line(
.....................314
Param
...................333
Pol
........................336
PolarGC
...............336
PtChg(
..................338
PtOff(
....................338
PtOn(
....................338
PxChg(
.................340
PxOff(
...................340
PxOn(
...................340
PxTest(
.................340
RcGDB
.................343
RcPic
....................343
RectGC
............... 344
SeqG
................... 351
Shade(
................. 352
SimulG
................ 354
SlpFld
.................. 358
StGDB
................. 361
StPic
.................... 362
TanLn(
................. 366
Text(
.................... 366
Trace
................... 367
Vert
...................... 369
ZData
................... 371
ZDecm
................. 372
ZFit
...................... 373
ZIn
........................ 373
ZInt
...................... 374
ZOut
.................... 375
ZPrev
................... 375
ZRcl
..................... 376
ZSqr
..................... 376
ZStd
..................... 377
ZTrig
.................... 378
Lists
aug(
......................270
cSum(
..................278
Deltalst(
...............279
dimL
.....................282
dimL
..................282
Fill(
.......................295
Form(
...................298
List entry:
{ }
.........316
li
4
vc
......................316
prod
......................338
Select(
..................350
seq(
......................351
SetLEdit
.............. 351
sortA
................... 359
sortD
................... 359
Sortx
.................... 359
Sorty
.................... 359
sum
...................... 364
vc
4
li
...................... 369
Chapter 20: A to Z Function and Instruction Reference
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Mathematics, Algebra, and Calculus
abs
.......................267
Addition:
+
............267
and
.......................268
angle
....................269
Ans
......................269
arc(
.......................269
Assignment:
=
......270
Ü
...........................271
Bin
.......................272
4
Bin
......................272
ClrEnt
..................273
ClTbl
....................273
conj
......................275
cos
.......................276
cos
L
1
....................276
cosh
.....................277
cosh
L
1
..................277
Þ
...........................278
Dec
.......................278
4
Dec
.....................279
Degree
.................279
Degree entry:
¡
.....279
der1(
....................280
der2(
....................280
Division:
/
..............284
DMS entry:
'
.........285
4
DMS
....................285
dxDer1
.................288
dxNDer
.................288
e^
.........................288
Eng
.......................290
Eq
4
St(
...................290
Equal:
=
................290
Equal to:
==
..........291
Euler
....................291
eval
......................291
evalF(
...................292
Exponent:
E
..........292
Factorial:
!
............294
Fix
........................295
Float
.....................295
fMax(
....................296
fMin(
.....................296
fnInt(
....................296
fPart
.....................298
4
Frac
....................298
gcd(
......................299
Greater than:
>
.....300
Greater than or
equal to:
..........301
ß
............................302
Hex
.......................302
4
Hex
......................303
imag
.....................306
int
.........................308
inter(
.....................309
Inverse:
L
1
.............309
iPart
......................309
lcm(
......................311
Less than:
<
..........312
Less than or
equal to:
..........312
ln
..........................316
log
........................318
max(
.....................319
min(
......................320
mod(
.....................320
Multiplication:
¹
....321
nCr
.......................322
nDer(
....................323
Negation:
L
............323
Normal
.................324
not
....................... 325
Not equal to:
ƒ
..... 326
nPr
....................... 326
Ý
........................... 326
Oct
....................... 327
4
Oct
..................... 327
or
......................... 328
Percent:
%
........... 334
pEval(
.................. 334
4
Pol
...................... 336
PolarC
................. 336
Polar complex:
. 336
poly
..................... 337
Power:
^
.............. 337
Power of 10:
10
^
. 337
Radian
................. 341
Radian entry:
r
..... 341
real
...................... 343
4
Rec
..................... 343
RectC
.................. 344
RK
........................ 345
Root:
x
............... 346
rotL
...................... 347
rotR
..................... 347
round(
................. 348
Sci
........................ 349
shftL
.................... 353
shftR
.................... 353
sign
...................... 354
simult(
................. 354
sin
........................ 355
sin
L
1
..................... 355
sinh
...................... 356
sinh
L
1
................... 356
Solver(
................. 358
Square:
2
.............. 360
Square root:
...... 360
St
4
Eq(
.................. 361
Store to
variable:
......... 362
Subtraction:
N
....... 363
tan
........................ 364
tan
L
1
..................... 365
tanh
..................... 365
tanh
L
1
................... 365
xor
....................... 370
264
Chapter 20: A to Z Function and Instruction Reference
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Matrices
aug(
..................... 270
cnorm
.................. 273
cond
.................... 274
det
........................ 281
dim
....................... 281
dim
.................... 281
eigVc
................... 289
eigVl
.................... 289
Fill(
...................... 295
ident
.................... 304
LU(
....................... 318
Matrix entry:
[ ]
.... 319
mRAdd(
............... 321
multR(
................. 322
norm
.................... 323
rAdd(
....................340
randM(
.................342
ref
.........................344
rnorm
...................346
rref
.......................348
rSwap(
.................348
Transpose:
T
........367
Programming
Asm(
.................... 269
AsmComp(
.......... 270
AsmPrgm
............ 270
CILCD
.................. 273
DelVar(
................ 280
Disp
..................... 283
DispG
.................. 283
DispT
................... 284
DS<(
.................... 288
Else
..................... 290
End
...................... 290
Equal:
=
............... 290
Equal to:
==
......... 291
For(
...................... 297
Get(
..................... 299
getKy
................... 300
Goto
.................... 300
IAsk
..................... 304
IAuto
................... 304
If
.......................... 305
InpSt
.................... 307
Input
.....................307
IS>(
.......................310
Lbl
........................311
LCust(
..................311
Menu(
...................320
Outpt(
...................329
Pause
...................333
Prompt
.................338
Repeat
.................345
Return
..................345
Send(
...................350
Stop
.....................362
Then
.....................366
While
....................369
Statistics
Box
...................... 272
ExpR
.................... 293
fcstx
..................... 294
fcsty
..................... 294
Hist
...................... 303
LgstR
................... 313
LinR
..................... 315
LnR
...................... 317
MBox
................... 319
OneVar
................ 327
P2Reg
.................. 330
P3Reg
.................. 331
P4Reg
.................. 332
PlOff
.................... 334
PlOn
.................... 334
Plot1(
................... 335
Plot2(
................... 335
Plot3(
................... 335
PwrR
................... 339
rand
..................... 341
randBin(
.............. 341
randInt(
................342
randM(
.................342
randNorm(
...........342
Scatter
.................349
Select(
..................350
SetLEdit
...............351
ShwSt
..................354
SinR
.....................357
Sortx
....................359
Sorty
....................359
StReg(
..................362
TwoVar
................368
xyline
...................370
Chapter 20: A to Z Function and Instruction Reference
265
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Strings
Concatenation:
+
.. 274
Eq
4
St(
.................. 290
lngth
.................... 316
St
4
Eq(
.................. 361
String entry:
"
.......363
sub(
......................363
Vectors
cnorm
.................. 273
cross(
.................. 277
4
Cyl
...................... 278
CylV
..................... 278
dim
...................... 281
dim
.................... 281
dot(
...................... 285
Fill(
...................... 295
li
4
vc
..................... 316
norm
.................... 323
RectV
.................. 344
rnorm
.................. 346
4
Sph
.....................360
SphereV
...............360
unitV
....................368
vc
4
li
......................369
Vector entry:
[ ]
....369
266
Chapter 20: A to Z Function and Instruction Reference
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Alphabetical Listing of Operations
All the operations in this section are included in the
CATALOG
. Non-alphabetic operations
(such as
+
,
!
, and
>
) are listed at the end of the
CATALOG
. In this A to Z Reference, however,
these operations are listed under their alphabetic equivalent (such as addition, factorial,
and greater than).
You always can use the
CATALOG
to select an operation and paste it to the home screen or
to a command line in the program editor. You also can use the specific keystrokes, menus,
or screens listed in this section.
Indicates menus or screens that paste the operation’s name only if you are in the
program editor. In most cases, you can use these menus or screens from the home
screen to perform the operation interactively, without pasting the name.
Indicates menus or screens that
are valid only from the program
editor’s main menu. From the
home screen, you cannot use
these menus or screens to select
an operation.
The syntax for some operations uses brackets [ ] to indicate optional arguments. If you use
an optional argument, do not enter the brackets.
program editor’s
main menu
Chapter 20: A to Z Function and Instruction Reference
267
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abs
MATH NUM menu
CPLX menu
MATRX CPLX menu
VECTR CPLX menu
abs
realNumber
or
abs (
realExpression
)
Returns the absolute value of
realNumber
or
realExpression
.
abs (
complexNumber
)
Returns the magnitude (modulus) of
complexNumber
.
abs (
real
,
imaginary
)
returns (
real
2
+
imaginary
2
)
.
abs (
magnitude
±
angle
)
returns
magnitude
.
abs
L
256.4
b
256.4
abs
L
4
3+13
b
25
abs (
L
4
3+13)
b
1
abs (3,4)
b
5
abs (3
±
4)
b
3
abs
list
abs
matrix
abs
vector
Returns a list, matrix, or vector in which each element is
the absolute value of the corresponding real or complex
element in the argument.
abs {1.25,
L
5.67}
b
{1.25 5.67}
abs [(3,4),(3
±
4)]
b
[5 3]
Addition:
+
\
numberA
+
numberB
Returns the sum of two real or complex numbers.
In
RectC
complex number mode:
(2,5)+(5,9)
b
(7,14)
number
+
list
Returns a list in which a real or complex
number
is
added to each element of a real or complex
list
.
4+{1,2,3}
b
{5 6 7}
3+{1,7,(2,1)}
b
{(4,0) (10,0) (5,1)}
268
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listA
+
listB
matrixA
+
matrixB
vectorA
+
vectorB
Returns a list, matrix, or vector that is the sum of the
corresponding real or complex elements in the
arguments. The two arguments must have the same
dimension.
For information about adding two strings, refer to
Concatenation
on page 274.
{1,2,3}+{4,5,6}
b
{5 7 9}
[[1,2,3][4,5,6]]+[[4,5,6][7,8,9]]
b
[[5 7 9 ]
[11 13 15]]
[1,2,3]+[4,5,6]
b
[5 7 9]
and
BASE BOOL menu
integerA
and
integerB
Compares two real integers bit by bit. Internally, both
integers are converted to binary. When corresponding
bits are compared, the result is 1 if both bits are 1;
otherwise, the result is 0. The returned value is the sum
of the bit results.
For example, 78
and
23 = 6.
78 = 1001110
Ü
23 = 0010111
Ü
0000110
Ü
=6
You can enter real numbers instead of integers, but they
are truncated automatically before the comparison.
In
Dec
number base mode:
78 and 23
b
6
In
Bin
number base mode:
1001110 and 10111
b
110
Ü
Ans
4
Dec
b
6
Þ
Chapter 20: A to Z Function and Instruction Reference
269
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angle
CPLX menu
MATRX CPLX menu
VECTR CPLX menu
angle (
complexNumber
)
Returns the polar angle of
complexNumber
, adjusted by
+
p
in the 2nd quadrant or
Lp
in the 3rd quadrant. The
polar angle of a real number is always 0.
angle (
real
,
imaginary
)
returns
tan
L
1
(
imaginary
/
real
)
.
angle (
magnitude
±
angle
)
returns
angle
,
Lp
<
angle
p
.
In
Radian
angle mode and
PolarC
complex
number mode:
angle (3,4)
b
.927295218002
angle (3
±
2)
b
2
(6
±p
/3)
A
b
(6
±
1.0471975512)
angle A
b
1.0471975512
angle
complexList
angle
complexMatrix
angle
complexVector
Returns a list, matrix, or vector in which each element is
the polar angle of the corresponding element in the
argument.
If
complexVector
has only two real elements, the
returned value is a real number, not a vector.
angle {(3,4),(3
±
2)}
b
{.927295218002 2}
Ans
-
¡
Ans
Returns the last answer.
1.7
¹
4.2
b
7.14
147/Ans
b
20.5882352941
arc(
CALC menu
arc (
expression
,
variable
,
start
,
end
)
Returns the length along
expression
with respect to
variable
, from
variable
=
start
to
variable
=
end
.
arc(x
2
,x,0,1)
b
1.47894285752
arc(cos x,x,0,
p
)
b
3.82019778904
Asm(
CATALOG
Asm(
assemblyProgramName
)
Executes an assembly language program. For more
information, refer to Chapter 16.
270
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AsmComp(
CATALOG
AsmComp(
AsciiAssemblyPrgmName
,
HexAssemblyPrgmName
)
Compiles an assembly language program written in
ASCII and stores the hex version. The compiled hex
version, which uses about half the storage space of the
ASCII version, cannot be edited.
When you execute the ASCII version, the TI
-
86 compiles
it each time. To speed up execution, use
AsmComp(
to
compile the ASCII version once and then execute the
hex version each time you want to run the program.
AsmPrgm
CATALOG
AsmPrgm
Must be used as the first line of an assembly language
program.
Assignment:
=
1
ã
=
ä
equationVariable
=
expression
Stores
expression
to
equationVariable
, without
evaluating
expression
. (If you use
X
to store an
expression to a variable, the expression is evaluated and
then the result is stored.)
y1=2 x
2
+6 x
N
5
b
Done
The built-in equation variables used for
graphing are case-sensitive. Use
y1
, not
Y1
.
aug(
LIST OPS menu
MATRX OPS menu
aug(
listA
,
listB
)
Returns a list consisting of
listB
appended
(concatenated) to the end of
listA
. The lists can be real
or complex.
aug({1,
L
3,2},{5,4})
b
{1
L
3 2 5 4}
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aug(matrixA,matrixB)
Returns a matrix consisting of
matrixB
appended as
new columns to the end of
matrixA
. The matrices can
be real or complex. Both must have the same number of
rows.
aug(matrix,vector)
Returns a matrix consisting of
vector
appended as a new
column to the end of
matrix
. The arguments can be real
or complex. The number of rows in
matrix
must equal
the number of elements in
vector
.
[[1,2,3][4,5,6]]
MATA
b
[[1 2 3]
[4 5 6]]
[[7,8][9,10]]
MATB
b
[[7 8 ]
[9 10]]
aug(MATA,MATB)
b
[[1 2 3 7 8 ]
[4 5 6 9 10]]
Axes(
GRAPH VARS menu
Axes(xAxisVariable,yAxisVariable)
Specifies the variables plotted for the axes in
DifEq
graphing mode. The
xAxisVariable
or
yAxisVariable
can be
t
,
Q1
through
Q9
, or
Q
¢
1
through
Q
¢
9
.
Axes(Q1,Q2)
b
Done
AxesOff
graph format screen
AxesOff
Turns off the graph axes.
AxesOn
graph format screen
AxesOn
Turns on the graph axes.
Ü
BASE TYPE menu
integer
Ü
Designates a real
integer
as binary, regardless of the
number base mode setting.
In
Dec
number base mode:
10
Ü
b
2
10
Ü
+10
b
12
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Bin
mode screen
Bin
Sets binary number base mode. Results are displayed
with the
Ü
suffix. In any number base mode, you can
designate an appropriate value as binary, decimal,
hexadecimal, or octal by using the
Ü
,
Þ
,
ß
, or
Ý
designator, respectively, from the
BASE TYPE
menu.
In
Bin
number base mode:
10+
Úß
+10
Ý
+10
Þ
b
100011
Ü
4
Bin
BASE CONV menu
number
4
Bin
list
4
Bin
matrix
4
Bin
vector
4
Bin
Returns the binary equivalent of the real or complex
argument.
In
Dec
number base mode:
2
¹
8
b
16
Ans
4
Bin
b
10000
Ü
{1,2,3,4}
4
Bin
b
{1
Ü
10
Ü
11
Ü
100
Ü
}
Box
STAT DRAW menu
Box
xList
,
frequencyList
Draws a box plot on the current graph, using the real
data in
xList
and the frequencies in
frequencyList
.
Box
xList
Uses frequencies of 1.
Box
Uses the data in built-in variables
xStat
and
fStat
. These
variables must contain valid data of the same
dimension; otherwise, an error occurs.
Starting with a
ZStd
graph screen:
{1,2,3,4,5,9}
XL
b
{1 2 3 4 5 9}
{1,1,1,4,1,1}
FL
b
{1 1 1 4 1 1}
0
xMin:0
yMin
b
0
Box XL,FL
b
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Circl(
GRAPH DRAW menu
Circl(
x
,
y
,
radius
)
Draws a circle with center (
x
,
y
) and
radius
on the
current graph.
Starting with a
ZStd
graph screen:
ZSqr:Circl(1,2,7)
b
ClDrw
GRAPH DRAW menu
STAT DRAW menu
ClDrw
Clears all drawn elements from the current graph.
CILCD
program editor
I/O menu
ClLCD
Clears the home screen (LCD).
ClrEnt
MEM menu
ClrEnt
Clears the contents of the Last Entry storage area.
ClTbl
program editor
I/O menu
ClTbl
Clears all values from the current table if
Indpnt: Ask
(
IAsk
, page 304) is set.
cnorm
MATRX MATH menu
cnorm
matrix
Returns the column norm of a real or complex
matrix
.
For each column,
cnorm
sums the absolute values
(magnitudes of complex elements) of the elements in that
column and returns the largest of those column sums.
[[1,
L
2,3][4,5,
L
6]]
MAT
b
[[1
L
2 3 ]
[4 5
L
6]]
cnorm MAT
b
9
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cnorm vector
Returns the sum of the absolute values of the real or
complex elements in
vector
.
[
L
1,2,
L
3]
VEC
b
[
L
1 2
L
3]
cnorm VEC
b
6
Concatenation:
+
\
stringA
+
stringB
Returns a string consisting of
stringB
appended
(concatenated) to the end of
stringA
.
"your name:"
STR
b
your name:
"Enter "+STR
b
Enter your name:
cond
MATRX MATH menu
cond squareMatrix
Returns the condition number of a real or complex
squareMatrix
, which is calculated as:
cnorm squareMatrix
¹
cnorm squareMatrix
L
1
The condition number indicates how well-behaved
squareMatrix
is expected to be for certain matrix
functions, particularly inverse. For a well-behaved
matrix, the condition number is close to 1.
log(cond squareMatrix)
indicates the number of digits
that may be lost due to round-off errors in computing
the inverse.
For a matrix with no inverse,
cond
returns an error.
[[1,0,0][0,1,0][0,0,1]]
MAT1
b
[[1 0 0]
[0 1 0]
[0 0 1]]
cond MAT1
b
1
log (Ans)
b
0
[[1,2,3][4,5,6][7,8,9]]
MAT2
b
[[1 2 3]
[4 5 6]
[7 8 9]]
cond MAT2
b
1.8
E
14
log (Ans)
b
14.2552725051
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conj
CPLX menu
MATRX CPLX menu
VECTR CPLX menu
conj (
complexNumber
)
Returns the complex conjugate of
complexNumber
.
In
RectC
mode,
conj (
real
,
imaginary
)
returns
(
real
,
Limaginary
)
.
In
PolarC
mode,
conj (
magnitude
±
angle
)
returns
(
magnitude
±L
angle
)
,
Lp
<
angle
p
.
conj
complexList
conj
complexMatrix
conj
complexVector
Returns a complex list, matrix, or vector in which each
element is the complex conjugate of the original.
In
RectC
complex number mode:
conj (3,4)
b
(3,
L
4)
conj (3
±
2)
b
(
L
1.24844050964,
L
2.7…
In
PolarC
complex number mode:
conj (3
±
2)
b
(3
±
L
2)
conj (3,4)
b
(5
±
L
.927295218002)
conj {
L
2,(3,4)}
b
{(1.41421356237
±
L
1.5…
CoordOff
graph format screen
CoordOff
Turns off cursor coordinates so they are not displayed
at the bottom of a graph.
CoordOn
graph format screen
CoordOn
Displays cursor coordinates at the bottom of a graph.
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cos
>
cos
angle
or
cos (
expression
)
Returns the cosine of
angle
or
expression
, which can be
real or complex.
An angle is interpreted as degrees or radians according
to the current angle mode. In any angle mode, you can
designate an angle as degrees or radians by using the
¡
or
r
designator, respectively, from the
MATH ANGLE
menu.
In
Radian
angle mode:
cos
p
/2
b
L
.5
cos (
p
/2)
b
0
cos 45
¡
b
.707106781187
In
Degree
angle mode:
cos 45
b
.707106781187
cos (
p
/2)
r
b
0
The squareMatrix cannot
have repeated
eigenvalues.
cos
list
Returns a list in which each element is the cosine of the
corresponding element in
list
.
cos
squareMatrix
Returns a square matrix that is the matrix cosine of
squareMatrix
. The matrix cosine corresponds to the
result calculated using power series or Cayley-Hamilton
Theorem techniques. This is
not
the same as simply
calculating the cosine of each element.
In
Radian
angle mode:
cos {0,
p
/2,
p
}
b
{1 0
L
1}
In
Degree
angle mode:
cos {0,60,90}
b
{1 .5 0}
cos
L
1
-
|
cos
L
1
number
or
cos
L
1
(
expression
)
Returns the arccosine of
number
or
expression
, which
can be real or complex.
In
Radian
angle mode:
cos
L
1
.5
b
1.0471975512
In
Degree
angle mode:
cos
L
1
1
b
0
cos
L
1
list
Returns a list in which each element is the arccosine of
the corresponding element in
list
.
In
Radian
angle mode:
cos
L
1
{0,.5}
b
{1.57079632679,1.047…
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cosh
MATH HYP menu
cosh
number
or
cosh (
expression
)
Returns the hyperbolic cosine of
number
or
expression
,
which can be real or complex.
cosh 1.2
b
1.81065556732
cosh
list
Returns a list in which each element is the hyperbolic
cosine of the corresponding element in
list
.
cosh {0,1.2}
b
{1 1.81065556732}
cosh
L
1
MATH HYP menu
cosh
L
1
number
or
cos
L
1
(
expression
)
Returns the inverse hyperbolic cosine of
number
or
expression
, which can be real or complex.
cosh
L
1
1
b
0
cosh
L
1
list
Returns a list in which each element is the inverse
hyperbolic cosine of the corresponding element in
list
.
cosh
L
1
{1,2.1,3}
b
{0 1.37285914424 1.7…
cross(
VECTR MATH menu
cross(
vectorA
,
vectorB
)
Returns the cross product of two real or complex
vectors, where:
cross([a,b,c],[d,e,f]) = [bf
N
ce cd
N
af ae
N
bd]
Both vectors must have the same dimension (either 2 or
3 elements). A 2-D vector is treated as a 3-D vector with
0 as the third element.
cross([1,2,3],[4,5,6])
b
[
L
3 6
L
3]
cross([1,2],[3,4])
b
[0 0
L
2]
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cSum(
LIST OPS menu
cSum(
list
)
Returns a list of the cumulative sums of the real or
complex elements in
list
, starting with the first element.
cSum({1,2,3,4})
b
{1 3 6 10}
{10,20,30}
L1
b
{10 20 30}
cSum(L1)
b
{10 30 60}
4
Cyl
VECTR OPS menu
vector
4
Cyl
Displays a 2- or 3-element real
vector
result in
cylindrical form, [r
q
z], even if the display mode is not
set for cylindrical (
CylV
).
[
L
2,0]
4
Cyl
b
[2
3.14159265359 0]
[
L
2,0,1]
4
Cyl
b
[2
3.14159265359 1]
CylV
mode screen
CylV
Sets cylindrical vector coordinate mode (
[r
q
z]
).
In
CylV
vector coordinate mode and
Radian
angle mode:
[3,4,5]
b
[5
.927295218002 5]
Þ
BASE TYPE menu
number
Þ
Designates a real
number
as decimal, regardless of the
number base mode setting.
In
Bin
number base mode:
10
Þ
b
1010
Ü
10
Þ
+10
b
1100
Ü
Dec
mode screen
Dec
Sets decimal number base mode. In any number base
mode, you can designate an appropriate value as binary,
decimal, hexadecimal, or octal by using the
Ü
,
Þ
,
ß
, or
Ý
designator, respectively, from the
BASE TYPE
menu.
In
Dec
number base mode:
10+10
Ü
+
Úß
+10
Ý
b
35
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4
Dec
BASE CONV menu
number
4
Dec
list
4
Dec
matrix
4
Dec
vector
4
Dec
Returns the decimal equivalent of the real or complex
argument.
In
Hex
number base mode:
2
¹Ú
b
1
Ùß
Ans
4
Dec
b
30
Þ
{
Õ
,
Ö
,
×
,
Ø
,
Ù
}
4
Dec
b
{10
Þ
11
Þ
12
Þ
13
Þ
14
Þ
}
Degree
mode screen
Degree
Sets degree angle mode.
In
Degree
angle mode:
sin 90
b
1
sin (
p
/2)
b
.027412133592
Degree entry:
¡
MATH ANGLE menu
number
¡
or
(
expression
)
¡
Designates a real
number
or
expression
as degrees,
regardless of the angle mode setting.
In
Radian
angle mode:
cos 90
b
L
.448073616129
cos 90
¡
b
0
list
¡
Designates each element in
list
as degrees.
cos {45,90,180}
¡
b
{.707106781187 0
L
1}
Deltalst(
LIST OPS menu
(Deltal shows on menu)
Deltalst(
list
)
Returns a list containing the differences between
consecutive real or complex elements in
list
. This
subtracts the first element in
list
from the second
element, the second from the third, and so on. The
resulting list is always one element shorter than
list
.
Deltalst({20,30,45,70})
b
{10 15 25}
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DelVar(
program editor
CTL menu
(DelVa shows
on menu)
DelVar(
variable
)
Deletes the specified user-created
variable
from
memory.
You cannot use
DelVar(
to delete a program variable or
built-in variable.
2
A
b
2
(A+2)
2
b
16
DelVar(A)
b
Done
(A+2)
2
b
ERROR 14 UNDEFINED
der1(
CALC menu
der1(
expression
,
variable
,
value
)
Returns the first derivative of
expression
with respect
to
variable
at the real or complex
value
.
der1(x^3,x,5)
b
75
der1(
expression
,
variable
)
Uses the current value of
variable
.
3
x
b
3
der1(x^3,x)
b
27
der1(
expression
,
variable
,
list
)
Returns a list containing the first derivatives at the
values specified by the elements in
list
.
der1(x^3,x,{5,3})
b
{75 27}
der2(
CALC menu
der2(
expression
,
variable
,
value
)
Returns the second derivative of
expression
with
respect to
variable
at the real or complex
value
.
der2(x^3,x,5)
b
30
der2(
expression
,
variable
)
Uses the current value of
variable
.
3
x
b
3
der2(x^3,x)
b
18
der2(
expression
,
variable
,
list
)
Returns a list containing the second derivatives at the
values specified by the elements in
list
.
der2(x^3,x,{5,3})
b
{30 18}
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det
MATRX MATH menu
det
squareMatrix
Returns the determinant of
squareMatrix
. The result is
real for a real matrix, complex for a complex matrix.
[[1,2][3,4]]
MAT
b
[[1 2]
[3 4]]
det MAT
b
L
2
DifEq
mode screen
DifEq
Sets differential equation graphing mode.
dim
MATRX OPS menu
VECTR OPS menu
dim
matrix
Returns a list containing the dimensions (number of
rows and columns) of a real or complex
matrix
.
dim
vector
Returns the length (number of elements) of a real or
complex
vector
.
[[2,7,1][
L
8,0,1]]
MAT
b
[[2 7 1]
[
L
8 0 1]]
dim MAT
b
{2 3}
dim [
L
8,0,1]
b
3
dim
X
, then MATRX OPS
menu
X
, then VECTR OPS
menu
{
rows
,
columns
}
dim
matrixName
If
matrixName
does not exist, creates a new matrix
with the specified dimensions and fills it with zeros.
If
matrixName
exists, redimensions that matrix to the
specified dimensions. Existing elements within the new
dimensions are not changed; elements outside the new
dimensions are deleted. If additional elements are
created, they are filled with zeros.
[[2,7][
L
8,0]]
MAT
b
[[2 7]
[
L
8 0]]
{3,3}
dim MAT
b
{3 3}
MAT
b
[[2 7 0]
[
L
8 0 0]
[0 0 0]]
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#ofElementsdim vectorName
If
vectorName
does not exist, creates a new vector with
the specified #
ofElements
and fills it with zeros.
If
vectorName
exists, redimensions that vector to the
specified #
ofElements
. Existing elements within the
new dimension are not changed; elements outside the
new dimension are deleted. If additional elements are
created, they are filled with zeros.
DelVar(VEC)
b
Done
4
dim VEC
b
4
VEC
b
[0 0 0 0]
[1,2,3,4]
VEC
b
[1 2 3 4]
2
dim VEC
b
2
VEC
b
[1 2]
3
dim VEC
b
3
VEC
b
[1 2 0]
dimL
LIST OPS menu
dimL list
Returns the length (number of elements) of a real or
complex
list
.
dimL {2,7,
L
8,0}
b
4
1/dimL {2,7,
L
8,0}
b
.25
dimL
X
, then LIST OPS
menu
#ofElementsdimL listName
If
listName
does not exist, creates a new list with the
specified #
ofElements
and fills it with zeros.
If
listName
exists, redimensions that list to the
specified #
ofElements
. Existing elements within the
new dimension are not changed; elements outside the
new dimension are deleted. If additional elements are
created, they are filled with zeros.
3
dimL NEWLIST
b
3
NEWLIST
b
{0 0 0}
{2,7,
L
8,1}
L1
b
{2 7
L
8 1}
5
dimL L1
b
5
L1
b
{2 7
L
8 1 0}
2
dimL L1
b
2
L1
b
{2 7}
DirFld
graph format screen
(scroll down to second
screen)
DirFld
In
DifEq
graphing mode, turns on direction fields. To
turn off direction and slope fields, use
FldOff
.
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Disp
program editor
I/O menu
Disp
valueA
,
valueB
,
valueC
,
...
Displays each value. The values can include strings and
variable names.
Disp
Displays the home screen.
10
x
b
10
Disp x^3+3 x
N
6
b
1024
Done
"Hello"
STR
b
Hello
Disp STR+", Jan"
b
Hello, Jan
Done
DispG
GRAPH menu
program editor
I/O menu
DispG
Displays the current graph.
Program segment in
Func
graphing mode:
©
:y1=4cos x
:
L
10
xMin:10
xMax
:
L
5
yMin:5
yMax
:DispG
©
Function names are
case-sensitive. Use
y1
, not
Y1
.
To select from a list of window
variable names, press
-
w
/
/
*
.
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DispT
program editor
I/O menu
DispT
Displays the table.
Program segment in
Func
graphing mode:
©
:y1=4cos x
:DispT
©
Division:
/
F
numberA
/
numberB
or
(
expressionA
)
/
(
expressionB
)
Returns one argument divided by another. The
arguments can be real or complex.
L
98/4
b
L
24.5
L
98/(4
¹
3)
b
L
8.16666666667
number
/
list
or
(
expression
)
/
list
Returns a list in which each element is
number
or
expression
divided by the corresponding element in
list
.
100/{10,25,2}
b
{10 4 50}
list
/
number
or
list
/
(
expression
)
vector
/
number
or
vector
/
(
expression
)
Returns a list or vector in which each element of
list
or
vector
is divided by
number
or
expression
.
{120,92,8}/4
b
{30 23 2}
In
RectC
complex number mode:
[8,1,(5,2)]/2
b
[(4,0) (.5,0) (2.5,1…
listA
/
listB
Returns a list in which each element of
listA
is divided
by the corresponding element of
listB
. The lists must
have the same dimension.
{1,2,3}/{4,5,6}
b
{.25 .4 .5}
Function names are
case-sensitive. Use
y1
, not
Y1
.
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DMS entry:
'
MATH ANGLE menu
In a trig calculation, the
result of a DMS entry is
treated as degrees in the
Degree
angle mode only. It
is treated as radians in
Radian
angle mode.
degrees
'
minutes
'
seconds
'
Designates the entered angle is in DMS format.
degrees
(
999,999),
minutes
(< 60), and
seconds
(< 60, may
have decimal places) must be entered as real numbers,
not as variable names or expressions.
Do not use
¡
and " symbols to specify
degrees
and
seconds
. For example, 5
¡
59' is interpreted as implied
multiplication of 5
¡
¹ 59' according to the current angle
mode setting.
54'32'30'
b
54.5416666667
In
Degree
angle mode:
cos 54'32'30'
b
.580110760699
In
Radian
angle mode:
cos 54'32'30'
b
L
.422502666138
Do not
use the following notation; in
Degree
angle mode:
5
¡
59'
b
295
4
DMS
MATH ANGLE menu
angle
4
DMS
Displays
angle
in DMS format. The result is shown in
degrees¡minutes
'
seconds"
format, even though you use
degrees
'
minutes
'
seconds
' to enter a DMS angle.
In
Degree
angle mode:
45.371
4
DMS
b
45
¡
22'15.6"
54'32'30'
¹
2
b
109.083333333
Ans
4
DMS
b
109
¡
5'0"
dot(
VECTR MATH menu
dot(
vectorA
,
vectorB
)
Returns the dot product of two real or complex vectors.
dot([a,b,c],[d,e,f])
returns
a
¹
d
+
b
¹
e
+
c
¹
f
.
dot([1,2,3],[4,5,6])
b
32
DrawDot
graph format screen
DrawDot
Sets dot graphing format.
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DrawF
GRAPH DRAW menu
DrawF
expression
Draws
expression
(in terms of
x
) on the current graph.
In
Func
graphing mode:
ZStd:DrawF 1.25 x cos x
b
DrawLine
graph format screen
DrawLine
Sets connected line graphing format.
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DrEqu(
GRAPH menu
To enter the ' character for
the Q' variables, use the
CHAR MISC
menu.
DrEqu(
xAxisVariable
,
yAxisVariable
,
xList
,
yList
,
tList
)
In
DifEq
graphing mode, draws the solution to a set of
differential equations stored in the
Q'
variables
specified by
xAxisVariable
and
yAxisVariable
. If
direction fields are off (
FldOff
is selected), the initial
values must be stored also.
After the solution is drawn,
DrEqu(
waits for you to
move the cursor to a new initial value and press b
to draw the new solution.
You then are prompted to press
Y
(to specify another
initial value) or
N
(to stop).
For the last-drawn solution, the
x
,
y
, and
t
values
(beginning at their initial values) are stored to
xList
,
yList
, and
tList
, respectively.
DrEqu(
xAxisVariable
,
yAxisVariable
)
Does not store
x
,
y
, and
t
values for the solution.
In
DifEq
graphing mode, starting with a
ZStd
graph screen:
Q'1=Q2:Q'2=
L
Q1
b
Done
0
tMin:1
QI1:0
QI2
b
0
DrEqu(Q1,Q2,XL,YL,TL)
b
Move the cursor to a new initial value.
b
Press
N
to stop graphing. You can then
examine
XL
,
YL
, and
TL
.
DrInv
GRAPH DRAW menu
DrInv
expression
Draws the inverse of
expression
by plotting
x
values on
the y-axis and
y
values on the x-axis.
In
Func
graphing mode:
ZStd:DrInv 1.25 x cos x
b
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DS<(
program editor
CTL menu
:DS<(
variable
,
value
)
:
command-if-variable
value
:
commands
Decrements
variable
by 1. If the result is <
value
, skips
command-if-variable
value
.
If the result is
value
, then
command-if-variablevalue
is executed.
variable
cannot be a built-in variable.
Program segment:
©
:9
A
:Lbl Start
:Disp A
:DS<(A,5)
:Goto Start
:Disp "A is now <5"
©
dxDer1
mode screen
dxDer1
Sets
der1
as the current differentiation type.
der1
differentiates exactly and calculates the value for each
function in an expression. It is more accurate than
dxNDer
, but more restrictive in that only certain
functions are valid in the expression.
The current differentiation type is used by the
arc(
and
TanLn(
functions, as well as
interactive graphing operations
dy/dx
,
dr/d
q
,
dy/dt
,
dx/dt
,
ARC
,
TanLn
, and
INFLC
.
dxNDer
mode screen
dxNDer
Sets
nDer
as the current differentiation type.
nDer
differentiates numerically and calculates the value for
an expression. It is less accurate than
dxDer1
, but less
restrictive in the functions that are valid in the
expression.
The current differentiation type is used by the
arc(
and
TanLn(
functions, as well as
interactive graphing operations
dy/dx
,
dr/d
q
,
dy/dt
,
dx/dt
,
ARC
,
TanLn
, and
INFLC
.
e^
-
e^
power
or
e^(
expression
)
Returns
e
raised to
power
or
expression
. The argument
can be real or complex.
e^0
b
1
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e^list
Returns a list in which each element is
e
raised to the
power specified by the corresponding element in
list
.
e^{1,0,.5}
b
{2.71828182846 1 1.6…
The squareMatrix cannot
have repeated
eigenvalues.
e^squareMatrix
Returns a square matrix that is the matrix exponential
of
squareMatrix
. The matrix exponential corresponds
to the result calculated using power series or Cayley-
Hamilton Theorem techniques. This is
not
the same as
simply calculating the exponential of each element.
eigVc
MATRX MATH menu
The squareMatrix cannot
have repeated
eigenvalues.
eigVc squareMatrix
Returns a matrix containing the eigenvectors for a real
or complex
squareMatrix
, where each column in the
result corresponds to an eigenvalue. The eigenvectors
of a real matrix may be complex. Note that an
eigenvector is not unique; it may be scaled by any
constant factor. TI
-
86 eigenvectors are normalized.
In
RectC
complex number mode:
[[
L
1,2,5][3,
L
6,9][2,
L
5,7]]
MAT
b
[[
L
1 2 5]
[3
L
6 9]
[2
L
5 7]]
eigVc MAT
b
[[(.800906446592,0) …
[(
L
.484028886343,0)…
[(
L
.352512270699,0)…
eigVl
MATRX MATH menu
eigVl squareMatrix
Returns a list of the eigenvalues of a real or complex
squareMatrix
. The eigenvalues of a real matrix may be
complex.
In
RectC
complex number mode:
[[
L
1,2,5][3,
L
6,9][2,
L
5,7]]
MAT
b
[[
L
1 2 5]
[3
L
6 9]
[2
L
5 7]]
eigVl MAT
b
{(
L
4.40941084667,0) …
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Else
program editor
CTL menu
Refer to syntax information for
If
, beginning on page 305. See
the
If:Then:Else:End
syntax.
End
program editor
CTL menu
End
Identifies the end of a
While
,
For
,
Repeat
, or
If-Then-
Else
loop.
Eng
mode screen
Eng
Sets engineering notation mode, in which the power-of-
10 exponent is a multiple of 3.
In
Eng
notation mode:
123456789
b
123.456789
E
6
In
Normal
notation mode:
123456789
b
123456789
Eq
4
St(
STRNG menu
Eq
4
St(
equationVariable
,
stringVariable
)
Converts the contents of
equationVariable
to a string
and stores it to
stringVariable
. Be sure to specify an
equation variable, not an equation.
To create an equation variable, use an equal sign (=) to
define the variable. For example, enter
A=B
¹
C
, not
B
¹
C
A
.
A=B
¹
C
b
Done
5
B
b
5
2
C
b
2
A
b
10
Eq
4
St(A,STR)
b
Done
STR
b
B
¹
C
Equal:
=
1
ã
=
ä
Refer to syntax information for
Assignment
on page 270.
If you use
=
in an expression in which the first argument
is not a variable name at the beginning of a line, the
=
is
treated as
N
(.
Example of = treated as
N
(, where 4=6+1 is
evaluated as 4
N
(6+1):
4=6+1
b
L
3
For true/false comparison, use == instead:
4==6+1
b
0
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Equal to:
==
TEST menu
The == operator is used to
compare arguments, while
= is used to assign a value
or expression to a variable.
numberA
==
numberB
matrixA
==
matrixB
vectorA
==
vectorB
stringA
==
stringB
Tests whether the condition
argumentA
==
argumentB
is true or false. Numbers, matrices, and vectors can be
real or complex. If complex, the magnitude (modulus)
of each element is compared. Strings are case-sensitive.
If true (
argumentA
=
argumentB
), returns
1
.
If false (
argumentA
ƒ
argumentB
), returns
0
.
2+2==2+2
b
1
2+(2==2)+2
b
5
[1,2]==[3
N
2,
L
1+3]
b
1
"A"=="a"
b
0
listA
==
listB
Returns a list of
1
s and/or
0
s to indicate if each element
in
listA
is = the corresponding element in
listB
.
{1,5,9}=={1,
L
6,9}
b
{1 0 1}
Euler
graph format screen
(scroll down to
second screen)
Euler
In
DifEq
graphing mode, uses an algorithm based on the
Euler method to solve differential equations. Typically,
Euler
is less accurate than
RK
but finds the solutions
much quicker.
eval
MATH MISC menu
eval
xValue
Returns a list containing the
y
values of all defined and
selected functions evaluated at a real
xValue
.
Remember that built-in equation variables
y1
and
y2
are case-sensitive:
y1=x^3+x+5
b
Done
y2=2 x
b
Done
eval 5
b
{135 10}
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evalF(
CALC menu
evalF(
expression
,
variable
,
value
)
Returns the value of
expression
evaluated with respect
to
variable
at a real or complex
value
.
evalF(x^3+x+5,x,5)
b
135
evalF(
expression
,
variable
,
list
)
Returns a list containing the values of
expression
evaluated with respect to
variable
at each element in
list
.
evalF(x^3+x+5,x,{3,5})
b
{35 135}
Exponent:
E
C
number
E
power
or
(
expressionA
)
E
(
expressionB
)
Returns a real or complex
number
raised to the
power
of 10, where
power
is a real integer such that
L
999 <
power
< 999. Any
expressions
must evaluate to
appropriate values.
12.3456789
E
5
b
1234567.89
(1.78/2.34)
E
2
b
76.0683760684
list
E
power
or
list
E
(
expression
)
Returns a list in which each element is the
corresponding element in
list
raised to the
power
of 10.
{6.34,854.6}
E
3
b
{6340 854600}
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ExpR
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
ExpR
xList
,
yList
,
frequencyList
,
equationVariable
Fits an exponential regression model (y=ab
x
) to real
data pairs in
xList
and
yList
(
y
values must be > 0) and
frequencies in
frequencyList
. The regression equation is
stored to
equationVariable
, which must be a built-in
equation variable such as
y1
,
r1
, and
xt1
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
ExpR
xList
,
yList
,
equationVariable
Uses frequencies of 1.
ExpR
xList
,
yList
,
frequencyList
Stores the regression equation to
RegEq
only.
ExpR
xList
,
yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
In
Func
graphing mode:
{1,2,3,4,5}
L1
b
{1 2 3 4 5}
{1,20,55,230,742}
L2
b
{1 20 55 230 742}
ExpR L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
ExpR
equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
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ExpR
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
Factorial:
!
MATH PROB menu
number
!
or
(expression)
!
Returns the factorial of a real integer or non-integer,
where 0
integer
449 and 0
non-integer
449.9. For
a non-integer, the Gamma function is used to find the
factorial. An
expression
must evaluate to an appropriate
value.
6!
b
720
12.5!
b
1710542068.32
list
!
Returns a list in which each element is the factorial of
the corresponding element in
list
.
{6,7,8}!
b
{720 5040 40320}
fcstx
STAT menu
fcstx yValue
Based on the current regression equation (
ReqEq
),
returns the forecasted
x
at a real
yValue
.
fcsty
STAT menu
fcsty xValue
Based on the current regression equation (
ReqEq
),
returns the forecasted
y
at a real
xValue
.
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Fill(
LIST OPS menu
MATRX OPS menu
VECTR OPS menu
Fill(
number
,
listName
)
Fill(
number
,
matrixName
)
Fill(
number
,
vectorName
)
Replaces each element in an existing
listName
,
matrixName
, or
vectorName
with a real or complex
number
.
{3,4,5}
L1
b
{3 4 5}
Fill(8,L1)
b
Done
L1
b
{8 8 8}
Fill((3,4),L1)
b
Done
L1
b
{(3,4) (3,4) (3,4)}
Fix
mode screen
Fix
integer
or
Fix (
expression
)
Sets fixed decimal mode for
integer
number of decimal
places, where 0
integer
11. An
expression
must
evaluate to an appropriate integer.
Fix 3
b
Done
p
/2
b
1.571
Float
b
Done
p
/2
b
1.57079632679
FldOff
graph format screen
(scroll down to
second screen)
FldOff
In
DifEq
graphing mode, turns off the slope and
direction fields. To turn on slope fields, use
SlpFld
. To
turn on direction fields, use
DirFld
.
Float
mode screen
Float
Sets floating decimal mode.
In
Radian
angle mode:
Fix 11
b
Done
sin (
p
/6)
b
.50000000000
Float
b
Done
sin (
p
/6)
b
.5
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fMax(
CALC menu
fMax(
expression
,
variable
,
lower
,
upper
)
Returns the value at which a local maximum of
expression
with respect to
variable
occurs, between
real
lower
and
upper
values for
variable
.
The tolerance is controlled by the built-in variable
tol
,
whose default is 1
E
L
5. To view or set
tol,
press -
) to display the tolerance editor.
fMax(sin x,x,
L
p
,
p
)
b
1.57079632598
fMin(
CALC menu
fMin(
expression
,
variable
,
lower
,
upper
)
Returns the value at which a local minimum of
expression
with respect to
variable
occurs, between
real
lower
and
upper
bounds for
variable
.
The tolerance is controlled by the built-in variable
tol
,
whose default is 1
E
L
5. To view or set
tol,
press -
) to display the tolerance editor.
fMin(sin x,x,
L
p
,
p
)
b
L
1.57079632691
fnInt(
CALC menu
fnInt(
expression
,
variable
,
lower
,
upper
)
Returns the numerical function integral of
expression
with respect to
variable
, between real
lower
and
upper
bounds for
variable
.
The tolerance is controlled by the built-in variable
tol
,
whose default is 1
E
L
5. To view or set
tol,
press -
) to display the tolerance editor.
fnInt(x
2
,x,0,1)
b
.333333333333
FnOff
GRAPH VARS menu
FnOff
function#
,
function#
,
...
Deselects the specified equation function numbers.
FnOff 1,3
b
Done
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FnOff
Deselects all equation function numbers.
FnOff
b
Done
FnOn
GRAPH VARS menu
FnOn function#,function#,
...
Selects the specified equation function numbers, in
addition to any others already selected.
FnOn 1,3
b
Done
FnOn
Selects all equation function numbers.
FnOn
b
Done
For(
program editor
CTL menu
:For(variable,begin,end,step)
or
:For(variable,begin,end)
:loop :loop
:End :End
:commands :commands
Executes the commands in
loop
iteratively, where the
number of repetitions is controlled by
variable
. The first
time through the loop,
variable
=
begin
. At the
End
of
the loop,
variable
is incremented by
step
. The loop is
repeated until
variable
>
end
. If you do not specify
step
,
the default is 1.
You can specify values such that
begin
>
end
. If so, be
sure to specify a negative
step
.
Program segment:
©
For(A,0,8,2)
Disp A
2
End
©
Displays 0, 4, 16, 36, and 64.
©
For(A,0,8)
Disp A
2
End
©
Displays 0, 1, 4, 9, 16, 25, 36, 49, and 64.
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Form(
LIST OPS menu
Form("
formula
",
listName
)
Generates the contents of
listName
automatically,
based on the attached
formula
. If you express
formula
in terms of a list, you can generate one list based on the
contents of another.
The contents of
listName
are updated automatically if
you edit
formula
or edit a list referenced in
formula
.
{1,2,3,4}
L1
b
{1 2 3 4}
Form("10
¹
L1",L2)
b
Done
L2
b
{10 20 30 40}
{5,10,15,20}
L1
b
{5 10 15 20}
L2
b
{50 100 150 200}
Form("L1/5",L2)
b
Done
L2
b
{1 2 3 4}
fPart
MATH NUM menu
fPart
number
or
fPart (
expression
)
Returns the fractional part of a real or complex
number
or
expression
.
fPart 23.45
b
.45
fPart (
L
17.26
¹
8)
b
L
.08
fPart
list
fPart
matrix
fPart
vector
Returns a list, matrix, or vector in which each element
is the fractional part of the corresponding element in
the specified argument.
[[1,
L
23.45][
L
99.5,47.15]]
MAT
b
[[1
L
23.45]
[
L
99.5 47.15 ]]
fPart MAT
b
[[0
L
.45]
[
L
.5 .15 ]]
4
Frac
MATH MISC menu
number
4
Frac
Displays a real or complex
number
as its rational
equivalent, a fraction reduced to its simplest terms.
If
number
cannot be simplified or if the denominator is
more than four digits, the decimal equivalent is
returned.
1/3+2/7
b
.619047619048
Ans
4
Frac
b
13/21
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list
4
Frac
matrix
4
Frac
vector
4
Frac
Returns a list, matrix, or vector in which each element
is the rational equivalent of the corresponding element
in the argument.
{1/2+1/3,1/6
N
3/8}
L1
b
{.833333333333
L
.208…
Ans
4
Frac
b
{5/6
L
5/24}
Func
mode screen
Func
Sets function graphing mode.
gcd(
MATH MISC menu
gcd(integerA,integerB)
Returns the greatest common divisor of two
nonnegative integers.
gcd(18,33)
b
3
gcd(listA,listB)
Returns a list in which each element is the gcd of the
two corresponding elements in
listA
and
listB
.
gcd({12,14,16},{9,7,5})
b
{3 7 1}
Get(
program editor
I/O menu
Get(variable)
Gets data from a CBL or CBR System or another TI
-
86
and stores it to
variable
.
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getKy
program editor
I/O menu
getKy
Returns the key code for the last key pressed. If no key
has been pressed,
getKy
returns
0
. Refer to the TI
-
86
key code diagram in Chapter 16.
Program:
PROGRAM:CODES
:Lbl TOP
:getKy
KEY
:While KEY==0
: getKy
KEY
:End
:Disp KEY
:Goto TOP
To break the program, press
^
and then
*
.
Goto
program editor
CTL menu
Goto
label
Transfers (branches) program control to the
label
specified by an existing
Lbl
instruction.
Program segment:
©
:0
TEMP:1
J
:Lbl TOP
:TEMP+J
TEMP
:If J<10
:Then
: J+1
J
: Goto TOP
:End
:Disp TEMP
©
Greater than:
>
TEST menu
numberA
>
numberB
or
(
expressionA
)
>
(
expressionB
)
Tests whether the condition is true or false. The
arguments must be real numbers.
If true (
numberA
>
numberB
), returns
1
.
If false (
numberA
numberB
), returns
0
.
2>0
b
1
88>123
b
0
L
5>
L
5
b
0
(20
¹
5/2)>(18
¹
2)
b
1
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number
>
list
Returns a list of
1
s and/or
0
s to indicate if
number
is >
the corresponding element in
list
.
1>{1,
L
6,10}
b
{0 1 0}
listA
>
listB
Returns a list of
1
s and/or
0
s to indicate if each element
in
listA
is > the corresponding element in
listB
.
{1,5,9}>{1,
L
6,10}
b
{0 1 0}
Greater than or
equal to:
TEST menu
numberA
numberB
or
(
expressionA
)
(
expressionB
)
Tests whether the condition is true or false. The
arguments must be real numbers.
If true (
numberA
numberB
), returns
1
.
If false (
numberA
<
numberB
), returns
0
.
2
0
b
1
88
123
b
0
L
5
L
5
b
1
(20
¹
5/2)
(18
¹
2)
b
1
number
list
Returns a list of
1
s and/or
0
s to indicate if
number
is
the corresponding element in
list
.
1
{1,
L
6,10}
b
{1 1 0}
listA
listB
Returns a list of
1
s and/or
0
s to indicate if each element
in
listA
is
the corresponding element in
listB
.
{1,5,9}
{1,
L
6,10}
b
{1 1 0}
GridOff
graph format screen
GridOff
Turns off grid format so that grid points are not
displayed.
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GridOn
graph format screen
GridOn
Turns on grid format so that grid points are displayed in
rows and columns corresponding to the tick marks on
each axis.
GrStl(
CATALOG
GrStl(
function#
,
graphStyle#
)
Sets the graph style for
function#
. For
graphStyle#
,
specify an integer from
1
through
7
:
1
= » (line)
4
= ¿ (below)
7
= Â (dot)
2
= ¼ (thick)
5
= À (path)
3
= ¾ (above)
6
= Á (animate)
Depending on the graphing mode, some graph styles may
not be available.
In
Func
graphing mode:
y1=x sin x
b
Done
GrStl(1,4)
b
Done
ZStd
b
ß
BASE TYPE menu
integer
ß
Designates a real
integer
as hexadecimal, regardless of
the number base mode setting.
In
Dec
number base mode:
10
ß
b
16
10
ß
+10
b
26
Hex
mode screen
Hex
Sets hexadecimal number base mode. Results are
displayed with the
ß
suffix. In any number base mode,
you can designate an appropriate value as binary,
decimal, hexadecimal, or octal by using the
Ü
,
Þ
,
ß
, or
Ý
designator, respectively, from the
BASE TYPE
menu.
To enter hexadecimal numbers
Õ
through
Ú
, use the
BASE A-F
menu. Do not use 1 to type a letter.
In
Hex
number base mode:
Ú
+10
Ü
+10
Ý
+10
Þ
b
23
ß
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4
Hex
BASE CONV menu
number
4
Hex
list
4
Hex
matrix
4
Hex
vector
4
Hex
Returns the hexadecimal equivalent of the real or
complex argument.
In
Bin
number base mode:
1010
¹
1110
b
10001100
Ü
Ans
4
Hex
b
8
×ß
{100,101,110}
4
Hex
b
{4
ß
5
ß
6
ß
}
Hist
STAT DRAW menu
Hist
xList
,
frequencyList
Draws a histogram on the current graph, using the real
data in
xList
and the frequencies in
frequencyList
.
Hist
xList
Uses frequencies of 1.
Hist
Uses the data in built-in variables
xStat
and
fStat
. These
variables must contain valid data of the same
dimension; otherwise, an error occurs.
Starting with a
ZStd
graph screen:
{1,2,3,4,6,7}
XL
b
{1 2 3 4 6 7}
{1,6,4,2,3,5}
FL
b
{1 6 4 2 3 5}
0
xMin:0
yMin
b
0
Hist XL,FL
b
{1,1,2,2,2,3,3,3,3,3,3,4,4,5,5,5,
7,7}
XL
b
{1 1 2 2 2 3 3 3 3 3 …
ClDrw:Hist XL
b
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Horiz
GRAPH DRAW menu
Horiz
yValue
Draws a horizontal line on the current graph at
yValue
.
In a
ZStd
graph screen:
Horiz 4.5
b
IAsk
CATALOG
IAsk
Sets the table so that the user can enter individual
values for the independent variable.
IAuto
CATALOG
IAuto
Sets the table so that the TI
N
86 generates the
independent-variable values automatically, based on
values entered for
TblStart
and
@
Tbl
.
ident
MATRX OPS menu
ident
dimension
Returns the identity matrix of
dimension
rows ×
dimension
columns.
ident 4
b
[[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]]
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If
program editor
CTL menu
:If
condition
:
command-if-true
:
commands
If
condition
is true, executes
command-if-true
.
Otherwise, skips
command-if-true
. The
condition
is
true if it evaluates to any nonzero number, or false if it
evaluates to zero.
To execute multiple commands if
condition
is true, use
If:Then:End
instead.
Program segment:
©
:If x<0
:Disp "x is negative"
©
:If
condition
:Then
:
commands-if-true
:End
:
commands
If
condition
is true (nonzero), executes
commands-if-
true
from
Then
to
End
. Otherwise, skips
commands-if-
true
and continues with the next command following
End
.
Program segment:
©
:If x<0
:Then
: Disp "x is negative"
: abs(x)
x
:End
©
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:If condition
:Then
:commands-if-true
:Else
:commands-if-false
:End
:commands
If
condition
is true (nonzero), executes
commands-if-
true
from
Then
to
Else
and then continues with the next
command following
End
.
If
condition
is false (zero), executes
commands-if-false
from
Else
to
End
and then continues with the next
command following
End
.
Program segment:
©
:If x<0
:Then
: Disp "x is negative"
:Else
: Disp "x is positive or zero"
:End
©
imag
CPLX menu
imag (complexNumber)
Returns the imaginary (nonreal) part of
complexNumber
. The imaginary part of a real number is
always 0.
imag (real,imaginary)
returns
imaginary
.
imag (magnitude
±
angle)
returns
magnitude
sin
angle
.
imag (3,4)
b
4
imag (3
±
4)
b
L
2.27040748592
imag complexList
imag complexMatrix
imag complexVector
Returns a list, matrix, or vector in which each element
is the imaginary part of the original argument.
imag {
L
2,(3,4),(3
±
4)}
b
{0 4
L
2.27040748592}
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InpSt
program editor
I/O menu
InpSt
promptString
,
variable
Pauses a program, displays
promptString
, and waits for
the user to enter a response. The response is stored to
variable
always as a string. When entering the response,
the user should not enter quotation marks.
To prompt for a number or expression instead of a
string, use
Input
.
InpSt
variable
Displays
?
as the prompt.
Program segment:
©
:InpSt "Enter your name:",STR
©
Input
program editor
I/O menu
Input
promptString
,
variable
Pauses a program, displays
promptString
, and waits for
the user to enter a response. The response is stored to
variable
in the form in which the user enters it.
A number or expression is stored as a number or
expression.
A list, vector, or matrix is stored as a list, vector, or
matrix.
An entry enclosed in " marks is stored as a string.
Program segment:
©
:Input "Enter test score:",SCR
©
Input
variable
Displays
?
as the prompt.
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Input
Pauses a program, displays the graph screen, and lets
the user update
x
and
y
(or
r
and
q
in
PolarGC
graph
format) by moving the free-moving cursor. To resume
the program, press b.
Program segment in
RectGC
graph format:
©
:Input
:Disp x,y
©
Input "CBLGET",variable
Receives list data sent from a CBL or CBR System and
stores it to
variable
on the TI
N
86. Use this
"CBLGET"
syntax for both CBL and CBR.
You can receive data also by using
Get(
as described on
page 299.
Input "CBLGET",L1
b
Done
int
MATH NUM menu
int number
or
int (expression)
Returns the largest integer
number
or
expression
. The
argument can be real or complex.
For a negative non-integer,
int
returns the integer that is
one less than the integer part of the number. To return
the exact integer part, use
iPart
instead.
int 23.45
b
23
int
L
23.45
b
L
24
int list
int matrix
int vector
Returns a list, matrix, or vector in which each element
is the largest integer less than or equal to the
corresponding element in the specified argument.
[[1.25,
L
23.45][
L
99,47.15]]
MAT
b
[[1.25
L
23.45]
[
L
99 47.15 ]]
int MAT
b
[[1
L
24]
[
L
99 47 ]]
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inter(
† MATH menu
inter(
x1
,
y1
,
x2,y2
,
xValue
)
Calculates the line through points (
x1
,
y1
) and (
x2
,
y2
)
and then interpolates or extrapolates a
y
value for the
specified
xValue
.
Using points (3,5) and (4,4), find the y value at
x=1:
inter(3,5,4,4,1)
b
7
inter(
y1
,
x1
,
y2,x2
,
yValue
)
Interpolates or extrapolates an
x
value for the specified
yValue
. Notice that points (
x1
,
y1
) and (
x2
,
y2
) must be
entered as (
y1
,
x1
) and (
y2
,
x2
).
Using points (
L
4,
L
7) and (2,6), find the x value
at y=10:
inter(
L
7,
L
4,6,2,10)
b
3.84615384615
Inverse:
L
1
-
ƒ
number
L
1
or
(
expression
)
L
1
Returns 1 divided by a real or complex
number
, where
number
ƒ
0.
5
L
1
b
.2
(10
¹
6)
L
1
b
.016666666667
list
L
1
Returns a list in which each element is 1 divided by the
corresponding element in
list
.
{
L
.5,10,2/8}
L
1
b
{
L
2 .1 4}
squareMatrix
L
1
Returns an inverted
squareMatrix
, where det
ƒ
0.
[[1,2][3,4]]
L
1
b
[[
L
2 1 ]
[1.5
L
.5]]
iPart
MATH NUM menu
iPart
number
or
iPart (
expression
)
Returns the integer part of
number
or
expression
. The
argument can be real or complex.
iPart 23.45
b
23
iPart
L
23.45
b
L
23
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iPart list
iPart matrix
iPart vector
Returns a list, matrix, or vector in which each element
is the integer part of the corresponding element in the
specified argument.
[[1.25,
L
23.45][
L
99.5,47.15]]
MAT
b
[[1.25
L
23.45]
[
L
99.5 47.15 ]]
iPart MAT
b
[[1
L
23]
[
L
99 47 ]]
IS>(
program editor
CTL menu
:IS>(variable,value)
:command-if-variable
value
:commands
Increments
variable
by 1. If the result is >
value
, skips
command-if-variable
value
.
If the result is
value
, then
command-if-variablevalue
is executed.
variable
cannot be a built-in variable.
Program segment:
©
:0
A
:Lbl Start
:Disp A
:IS>(A,5)
:Goto Start
:Disp "A is now >5"
©
LabelOff
graph format screen
LabelOff
Turns off axes labels.
LabelOn
graph format screen
LabelOn
Turns on axes labels.
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311
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Lbl
program editor
CTL menu
Lbl
label
Creates a
label
of up to eight characters. A program can
use a
Goto
instruction to transfer control (branch) to a
specified label.
Program segment, assuming a correct
password has already been stored to the
password
variable:
©
:Lbl Start
:InpSt "Enter password:",PSW
:If PSW
ƒ
password
:Goto Start
:Disp "Welcome"
©
lcm(
MATH MISC menu
lcm(
integerA
,
integerB
)
Returns the least common multiple of two nonnegative
integers.
lcm(5,2)
b
10
lcm(6,9)
b
18
lcm(18,33)
b
198
LCust(
program editor
CTL menu
LCust(
item#
,"
title
"
[
,
item#
,"
title
",
...]
)
Loads (defines) the TI
N
86’s custom menu, which is
displayed when the user presses 9. The menu can
have up to 15 items, shown in three groups of five items.
For each
item#
/
title
pair:
item#
— integer from 1 through 15 that identifies the
item’s position in the menu. The item numbers must
be specified in order, but you can skip numbers.
"
title
"
— string with up to 8 characters (not counting
the quotes) that will be pasted to the current cursor
location when the item is selected. This can be a
variable name, expression, function name, program
name, or any text string.
Program segment:
©
:LCust(1,"t",2,"Q'1",3,"Q'2",4,"R
K",5,"Euler",6,"QI1",7,"QI2",8,"t
Min")
©
After executed and when the user presses
9
:
InpSt
stores input as a string,
so be sure to store a string t
o
the
password
variable.
312
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Less than:
<
TEST menu
numberA
<
numberB
or
(
expressionA
)
<
(
expressionB
)
Tests whether the condition is true or false. The
arguments must be real numbers.
If true (
numberA
<
numberB
), returns
1
.
If false (
numberA
numberB
), returns
0
.
2<0
b
0
88<123
b
1
L
5<
L
5
b
0
(20
¹
5/2)<(18
¹
3)
b
1
number
<
list
Returns a list of
1
s and/or
0
s to indicate if
number
is <
the corresponding element in
list
.
1<{1,
L
6,10}
b
{0 0 1}
listA
<
listB
Returns a list of
1
s and/or
0
s to indicate if each element
in
listA
is < the corresponding element in
listB
.
{1,5,9}<{1,
L
6,10}
b
{0 0 1}
Less than or
equal to:
TEST menu
numberA
numberB
or
(
expressionA
)
(
expressionB
)
Tests whether the condition is true or false. The
arguments must be real numbers.
If true (
numberA
numberB
), returns
1
.
If false (
numberA
>
numberB
), returns
0
.
2
0
b
0
88
123
b
1
L
5
L
5
b
1
(20
¹
5/2)
(18
¹
3)
b
1
number
list
Returns a list of
1
s and/or
0
s to indicate if
number
is
the corresponding element in
list
.
1
{1,
L
6,10}
b
{1 0 1}
listA
listB
Returns a list of
1
s and/or
0
s to indicate if each element
in
listA
is
the corresponding element in
listB
.
{1,5,9}
{1,
L
6,10}
b
{1 0 1}
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LgstR
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
LgstR
returns a
tolMet
value that indicates if the
result meets the TI
-
86’s
internal tolerance.
If
tolMet
=
1
, the result is
within the internal
tolerance.
If
tolmet
=
0
, the result is
outside the internal
tolerance, although it
may be useful for general
purposes.
LgstR
[
iterations
,
]
xList
,
yList
,
frequencyList
,
equationVariable
Fits a logistic regression model (y=a/(1+be
cx
)+d) to real
data pairs in
xList
and
yList
and frequencies in
frequencyList
. The regression equation is stored to
equationVariable
, which must be a built-in equation
variable such as
y1
,
r1
, and
xt1
. The equation’s
coefficients always are stored as a list to built-in
variable
PRegC
.
The number of
iterations
is optional. If omitted, 64 is
the default. A large number of
iterations
may produce
more accurate results but may require longer
calculation times. A smaller number may produce less
accurate results but with shorter calculation times.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
In
Func
graphing mode:
{1,2,3,4,5,6}
L1
b
{1 2 3 4 5 6}
{1,1.3,2.5,3.5,4.5,4.8}
L2
b
{1 1.3 2.5 3.5 4.5 4…
LgstR L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
LgstR
[
iterations
,
]
xList
,
yList
,
equationVariable
Uses frequencies of 1.
LgstR
[
iterations
,
]
xList
,
yList
,
frequencyList
Stores the regression equation to
RegEq
only.
LgstR
[
iterations
,
]
xList
,
yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
314
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LgstR
[
iterations,
]
equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
LgstR
[
iterations
]
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
Line(
GRAPH DRAW menu
Line(x1,y1,x2,y2)
Draws a line from point (
x1
,
y1
) to (
x2
,
y2
).
In
Func
graphing mode and a
ZStd
graph
screen:
Line(
L
2,
L
7,9,8)
b
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LinR
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
LinR
xList
,
yList
,
frequencyList
,
equationVariable
Fits a linear regression model (y=a+bx) to real data
pairs in
xList
and
yList
and frequencies in
frequencyList
. The regression equation is stored to
equationVariable
, which must be a built-in equation
variable such as
y1
,
r1
, and
xt1
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
LinR
xList
,
yList
,
equationVariable
Uses frequencies of 1.
LinR
xList
,
yList
,
frequencyList
Stores the regression equation to
RegEq
only.
LinR
xList
,
yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
In
Func
graphing mode:
{1,2,3,4,5,6}
L1
b
{1 2 3 4 5 6}
{4.5,4.6,6,7.5,8.5,8.7}
L2
b
{4.5 4.6 6 7.5 8.5 8.7}
LinR L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
LinR
equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
316
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LinR
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
List entry:
{ }
LIST menu
{element1,element2,
...
}
Defines a list in which each element is a real or complex
number or variable.
{1,2,3}
L1
b
{1 2 3}
In
RectC
complex number mode:
{3,(2,4),8
¹
2}
L2
b
{(3,0) (2,4) (16,0)}
li
4
vc
LIST OPS menu
VECTR OPS menu
li
4
vc list
Returns a vector converted from a real or complex
list
.
li
4
vc {2,7,
L
8,0}
b
[2 7
L
8 0]
ln
B
ln number
or
ln (expression)
Returns the natural logarithm of a real or complex
number
or
expression
.
ln list
Returns a list in which each element is the natural
logarithm of the corresponding element in
list
.
ln 2
b
.69314718056
ln (36.4/3)
b
2.49595648597
In
RectC
complex number mode:
ln
L
3
b
(1.09861228867,3.141…
ln {2,3}
b
{.69314718056 1.0986…
lngth
STRNG menu
lngth string
Returns the length (number of characters) of
string
.
The character count includes spaces but not quotation
marks.
lngth "The answer is:"
b
14
"The answer is:"
STR
b
The answer is:
lngth STR
b
14
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LnR
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
LnR
xList
,
yList
,
frequencyList
,
equationVariable
Fits a logarithmic regression model (y=a+b ln x) to the
real data pairs in
xList
and
yList
(
x
values must be > 0)
and frequencies in
frequencyList
. The regression
equation is stored to
equationVariable
, which must be a
built-in equation variable such as
y1
,
r1
, and
xt1
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
LnR
xList
,
yList
,
equationVariable
Uses frequencies of 1.
LnR
xList
,
yList
,
frequencyList
Stores the regression equation to
RegEq
only.
LnR
xList
,
yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
In
Func
graphing mode:
{1,2,3,4,5,6}
L1
b
{1 2 3 4 5 6}
{.6,1.5,3.8,4.2,4.3,5.9}
L2
b
{.6 1.5 3.8 4.2 4.3 5.9}
LnR L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
LnR
equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
318
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LnR
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
log
<
log number
or
log (expression)
Returns the logarithm of a real or complex
number
or
expression
, where:
10
logarithm
=
number
log 2
b
.301029995664
log (36.4/3)
b
1.08398012893
In
RectC
complex number mode:
log (3,4)
b
(.698970004336,.4027…
log list
Returns a list in which each element is the logarithm of
the corresponding element in
list
.
In
RectC
complex number mode:
log {
L
3,2}
b
{(.47712125472,1.364…
LU(
MATRX MATH menu
LU(matrix,lMatrixName, uMatrixName, pMatrixName)
Calculates the Crout LU (lower-upper) decomposition
of a real or complex
matrix
. The lower triangular
matrix is stored in
lMatrixName
, the upper triangular
matrix in
uMatrixName
, and the permutation matrix
(which describes the row swaps done during the
calculation) in
pMatrixName
.
lMatrixName
¹
uMatrixName
=
pMatrixName
¹
matrix
[[6,12,18][5,14,31][3,8,18]]
MAT
b
[[6 12 18]
[5 14 31]
[3 8 18]]
LU(MAT,L,U,P)
b
Done
L
b
[[6 0 0]
[5 4 0]
[3 2 1]]
U
b
[[1 2 3]
[0 1 4]
[0 0 1]]
P
b
[[1 0 0]
[0 1 0]
[0 0 1]]
Chapter 20: A to Z Function and Instruction Reference
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Matrix entry:
[ ]
-
and
-
[
[
row1
]
[
row2
]
...
]
Defines a matrix entered row-by-row in which each
element is a real or complex number or variable.
Enter each
[
row
]
as
[
element
,
element
, ...
]
.
[[1,2,3][4,5,6]]
MAT
b
[[1 2 3]
[4 5 6]]
max(
MATH NUM menu
max(
numberA
,
numberB
)
Returns the larger of two real or complex numbers.
max(2.3,1.4)
b
2.3
max(
list
)
Returns the largest element in
list
.
max({1,9,
p
/2,e^2})
b
9
max(
listA
,
listB
)
Returns a list in which each element is the larger of the
corresponding elements in
listA
and
listB
.
max({1,10},{2,9})
b
{2 10}
MBox
STAT DRAW menu
MBox
xList
,
frequencyList
Draws a modified box plot on the current graph, using
the real data in
xList
and the frequencies in
frequencyList
.
MBox
xList
Uses frequencies of 1.
MBox
Uses the data in built-in variables
xStat
and
fStat
. These
variables must contain valid data of the same
dimension; otherwise, an error occurs.
Starting with a
ZStd
graph screen:
{1,2,3,4,5,9}
XL
b
{1 2 3 4 5 9}
{1,1,1,4,1,1}
FL
b
{1 1 1 4 1 1}
0
xMin:0
yMin
b
0
MBox XL,FL
b
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Menu(
program editor
CTL menu
Menu(
item#
,"
title1
",
label1
[
,
...
,
item#
,"
title15
",
label15
]
)
Generates a menu of up to 15 items during program
execution. Menus are displayed as three groups of five
items. For each item:
item#
— integer from 1 through 15 that identifies this
item’s position in the menu.
"
title
"
— text string that will be displayed for this
item on the menu. Typically, use from 1 through 5
characters; additional characters may not be seen on
the menu.
label
— valid label to which program execution will
branch when the user selects this item.
Program segment:
©
:Lbl A
:Input "Radius:",RADIUS
:Disp "Area is:",
p
¹
RADIUS
2
:Menu(1,"Again",A,5,"Stop",B)
:Lbl B
:Disp "The End"
Example when executed:
min(
MATH NUM menu
min(
numberA
,
numberB
)
Returns the smaller of two real or complex numbers.
min(3,
L
5)
b
L
5
min(
L
5.2,
L
5.3)
b
L
5.3
min(5,2+2)
b
4
min(
list
)
Returns the smallest element in
list
.
min({1,3,
L
5})
b
L
5
min(
listA
,
listB
)
Returns a list in which each element is the smaller of
the corresponding elements in
listA
and
listB
.
min({1,2,3},{3,2,1})
b
{1 2 1}
mod(
MATH NUM menu
mod(
numberA
,
numberB
)
Returns
numberA
modulo
numberB
. The arguments
must be real.
mod(7,0)
b
7
mod(7,3)
b
1
mod(
L
7,3)
b
2
mod(7,
L
3)
b
L
2
mod(
L
7,
L
3)
b
L
1
Chapter 20: A to Z Function and Instruction Reference
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mRAdd(
MATRX OPS menu
mRAdd(
number
,
matrix
,
rowA
,
rowB
)
Returns the result of a “multiply and add row” matrix
operation, where:
a.
rowA
of a real or complex
matrix
is multiplied by a
real or complex
number
.
b. The results are added to (and then stored in)
rowB
.
[[5,3,1][2,0,4][3,
L
1,2]]
MAT
b
[[5 3 1]
[2 0 4]
[3
L
1 2]]
mRAdd(5,MAT,2,3)
b
[[5 3 1 ]
[2 0 4 ]
[13
L
1 22]]
Multiplication:
¹
M
numberA
¹
numberB
Returns the product of two real or complex numbers.
2
¹
5
b
10
number
¹
list
or
list
¹
number
number
¹
matrix
or
matrix
¹
number
number
¹
vector
or
vector
¹
number
Returns a list, matrix, or vector in which each element
is
number
multiplied by the corresponding element in
list
,
matrix
, or
vector
.
4
¹
{10,9,8}
b
{40 36 32}
In
RectC
complex number mode:
[8,1,(5,2)]
¹
3
b
[(24,0) (3,0) (15,6)]
listA
¹
listB
Returns a list in which each element of
listA
is
multiplied by the corresponding element of
listB
. The
lists must have the same dimension.
{1,2,3}
¹
{4,5,6}
b
{4 10 18}
matrix
¹
vector
Returns a vector in which
matrix
is multiplied by
vector
. The number of columns in
matrix
must equal
the number of elements in
vector
.
[[1,2,3][4,5,6]]
MAT
b
[[1 2 3]
[4 5 6]]
MAT
¹
[7,8,9]
b
[50 122]
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matrixA ¹ matrixB
Returns a matrix in which
matrixA
is multiplied by
matrixB
. The number of columns in
matrixA
must
equal the number of rows in
matrixB
.
[[2,2][3,4]]
MATA
b
[[2 2]
[3 4]]
[[1,2,3][4,5,6]]
MATB
b
[[1 2 3]
[4 5 6]]
MATA
¹
MATB
b
[[10 14 18]
[19 26 33]]
multR(
MATRX OPS menu
multR(
number
,
matrix
,
row
)
Returns the result of a “row multiplication” matrix
operation, where:
a. The specified
row
of a real or complex
matrix
is
multiplied by a real or complex
number
.
b. The results are stored in the same
row
.
[[5,3,1][2,0,4][3,
L
1,2]]
MAT
b
[[5 3 1]
[2 0 4]
[3
L
1 2]]
multR(5,MAT,2)
b
[[5 3 1 ]
[10 0 20]
[3
L
1 2 ]]
nCr
MATH PROB menu
items
nCr
number
Returns the number of combinations of
items
(
n
) taken
number
(
r
) at a time. Both arguments must be real
nonnegative integers.
5 nCr 2
b
10
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nDer(
CALC menu
To view or set the value for
d
, press
-
)
to
display the tolerance
screen.
nDer(
expression
,
variable
,
value
)
Returns an approximate numerical derivative of
expression
with respect to
variable
evaluated at a real
or complex
value
. The approximate numerical
derivative is the slope of the secant line through the
points:
(
value
Nd
,f(
value
Nd
)) and (
value+
d
,f(
value
+
d
))
As the step value
d
gets smaller, the approximation
usually gets more accurate.
For
d
=.001:
nDer(x^3,x,5)
b
75.000001
For
d
=1
E
L
4:
nDer(x^3,x,5)
b
75
nDer(
expression
,
variable
)
Uses the current value of
variable
.
5
x
b
5
nDer(x^3,x)
b
75
Negation:
L
a
L
number
or
L
(
expression
)
L
list
L
matrix
L
vector
Returns the negative of the real or complex argument.
L
2+5
b
3
L
(2+5)
b
L
7
L
{0,
L
5,5}
b
{0 5
L
5}
norm
MATRX MATH menu
VECTR MATH menu
norm
matrix
Returns the Frobenius norm of a real or complex
matrix
, calculated as:
G
(
real
2
+
imaginary
2
)
where the sum is over all elements.
[[1,
L
2][
L
3,4]]
MAT
b
[[1
L
2]
[
L
3 4 ]]
norm MAT
b
5.47722557505
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norm vector
Returns the length of a real or complex
vector
, where:
norm [a,b,c]
returns
a
2
+b
2
+c
2
.
norm [3,4,5]
b
7.07106781187
norm number
or
norm (expression)
norm list
Returns the absolute value of a real or complex
number
or
expression
, or of each element in
list
.
norm
L
25
b
25
In
Radian
angle mode:
norm {
L
25,cos
L
(
p
/3)}
b
{25 .5}
Normal
mode screen
Normal
Sets normal notation mode.
In
Eng
notation mode:
123456789
b
123.456789
E
6
In
Sci
notation mode:
123456789
b
1.23456789
E
8
In
Normal
notation mode:
123456789
b
123456789
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not
BASE BOOL menu
not
integer
Returns the one’s complement of a real
integer
.
Internally,
integer
is represented as a 16-bit binary
number. The value of each bit is flipped (0 becomes 1,
and vice versa) for the one’s complement.
For example,
not
78:
78 = 0000000001001110
Ü
1111111110110001
Ü
(one’s complement)
To find the magnitude of a negative binary number,
determine its two’s complement (take the one’s
complement and then add 1). For example:
1111111110110001
Ü
= one’s complement of 78
0000000001001110
Ü
(one’s complement)
+ 0000000000000001
Ü
0000000001001111
Ü
= 79 (two’s complement)
Therefore,
not
78 =
L
79.
You can enter real numbers instead of integers, but they
are truncated automatically before the comparison.
In
Dec
number base mode:
not 78
b
L
79
In
Bin
number base mode:
not 1001110
b
1111111110110001
Ü
Ans
4
Dec
b
L
79
Þ
Sign bit; 1 indicates a negative number
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Not equal to:
ƒ
TEST menu
numberA
ƒ
numberB
matrixA
ƒ
matrixB
vectorA
ƒ
vectorB
stringA
ƒ
stringB
Tests whether the condition
argumentA
ƒ
argumentB
is true or false. Numbers, matrices, and vectors can be
real or complex. If complex, the magnitude (modulus)
of each element is compared. Strings are case-sensitive.
If true (
argumentA
ƒ
argumentB
), returns
1
.
If false (
argumentA
=
argumentB
), returns
0
.
2+2
ƒ
3+2
b
1
2+(2
ƒ
3)+2
b
5
[1,2]
ƒ
[3
N
2,
L
1+3]
b
0
"A"
ƒ
"a"
b
1
listA
ƒ
listB
Returns a list of
1
s and/or
0
s to indicate if each element
in
listA
is
ƒ
the corresponding element in
listB
.
{1,5,9}
ƒ
{1,
L
6,9}
b
{0 1 0}
nPr
MATH PROB menu
items
nPr
number
Returns the number of permutations of
items
(
n
) taken
number
(
r
) at a time. Both arguments must be real
nonnegative integers.
5 nPr 2
b
20
Ý
BASE TYPE menu
integer
Ý
Designates a real
integer
as octal, regardless of the
number base mode setting.
In
Dec
number base mode:
10
Ý
b
8
10
Ý
+10
b
18
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Oct
mode screen
Oct
Sets octal number base mode. Results are displayed
with the
Ý
suffix. In any number base mode, you can
designate an appropriate value as binary, decimal,
hexadecimal, or octal by using the
Ü
,
Þ
,
ß
, or
Ý
designator, respectively, from the
BASE TYPE
menu.
In
Oct
number base mode:
10+10
Ü
+
Úß
+10
Þ
b
43
Ý
4
Oct
BASE CONV menu
number
4
Oct
list
4
Oct
matrix
4
Oct
vector
4
Oct
Returns the octal equivalent of the real or complex
argument.
In
Dec
number base mode:
2
¹
8
b
16
Ans
4
Oct
b
20
Ý
{7,8,9,10}
4
Oct
b
{7
Ý
10
Ý
11
Ý
12
Ý
}
OneVar
STAT CALC menu
(OneVa shows on menu)
OneVar
xList
,
frequencyList
Performs one-variable statistical analysis using real data
points in
xList
and frequencies in
frequencyList
.
The values used for
xList
and
frequencyList
are stored
automatically to built-in variables
xStat
and
fStat
,
respectively.
OneVar
xList
Uses frequencies of 1.
{0,1,2,3,4,5,6}
XL
b
{0 1 2 3 4 5 6}
OneVar XL
b
Scroll down to see more results.
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OneVar
Uses
xStat
and
fStat
for
xList
and
frequencyList
. These
built-in variables must contain valid data of the same
dimension; otherwise, an error occurs.
or
BASE BOOL menu
integerA or integerB
Compares two real integers bit by bit. Internally, both
integers are converted to binary. When corresponding
bits are compared, the result is 1 if either bit is 1; the
result is 0 only if both bits are 0. The returned value is
the sum of the bit results.
For example, 78
or
23 = 95.
78 = 1001110
Ü
23 = 0010111
Ü
1011111
Ü
=95
You can enter real numbers instead of integers, but they
are truncated automatically before the comparison.
In
Dec
number base mode:
78 or 23
b
95
In
Bin
number base mode:
1001110 or 10111
b
1011111
Ü
Ans
4
Dec
b
95
Þ
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Outpt(
program editor
I/O menu
Outpt(
row
,
column
,
string
)
Displays
string
beginning at
row
and
column
, where
1
row
8 and 1
column
21.
Outpt(
row
,
column
,
value
)
Displays
value
beginning at the specified
row
and
column
.
Outpt("CBLSEND",
listName
)
Sends the contents of
listName
to the CBL or CBR
System.
You can send data also by using
Send(
as described on
page 350.
Program segment:
©
:ClLCD
:For(i,1,8)
: Outpt(i,randInt(1,21),"A")
:End
©
Example result after execution:
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P2Reg
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
P2Reg
xList
,
yList
,
frequencyList
,
equationVariable
Performs a second order polynomial regression using
real data pairs in
xList
and
yList
and frequencies in
frequencyList
. The regression equation is stored to
equationVariable
, which must be a built-in equation
variable such as
y1
,
r1
, and
xt1
. The equation’s
coefficients always are stored as a list to built-in
variable
PRegC
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
P2Reg
xList
,
yList
,
equationVariable
Uses frequencies of 1.
P2Reg
xList
,
yList
,
frequencyList
Stores the regression equation to
RegEq
only.
In
Func
graphing mode:
{1,2,3,4,5,6}
L1
b
{1 2 3 4 5 6}
{
L
2,6,11,23,29,47}
L2
b
{
L
2 6 11 23 29 47}
P2Reg L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
P2Reg
xList
,
yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
P2Reg
equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
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P2Reg
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
P3Reg
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
P3Reg xList,yList,frequencyList,equationVariable
Performs a third order polynomial regression using real
data pairs in
xList
and
yList
and frequencies in
frequencyList
. The regression equation is stored to
equationVariable
, which must be a built-in equation
variable such as
y1
,
r1
, and
xt1
. The equation’s
coefficients always are stored as a list to built-in
variable
PRegC
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
P3Reg xList,yList,equationVariable
Uses frequencies of 1.
P3Reg xList,yList,frequencyList
Stores the regression equation to
RegEq
only.
In
Func
graphing mode:
{1,2,3,4,5,6}
L1
b
{1 2 3 4 5 6}
{
L
6,15,27,88,145,294}
L2
b
{
L
6 15 27 88 145 294}
P3Reg L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
P3Reg xList,yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
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P3Reg equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
P3Reg
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
P4Reg
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
P4Reg xList,yList,frequencyList,equationVariable
Performs a fourth order polynomial regression using
real data pairs in
xList
and
yList
and frequencies in
frequencyList
. The regression equation is stored to
equationVariable
, which must be a built-in equation
variable such as
y1
,
r1
, and
xt1
. The equation’s
coefficients always are stored as a list to built-in
variable
PRegC
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
P4Reg xList,yList,equationVariable
Uses frequencies of 1.
P4Reg xList,yList,frequencyList
Stores the regression equation to
RegEq
only.
In
Func
graphing mode:
{
L
2,
L
1,0,1,2,3,4,5,6}
L1
b
{
L
2
L
1 0 1 2 3 4 5 6}
{4,3,1,2,3,2,2,4,6}
L2
b
{4 3 1 2 3 2 2 4 6}
P4Reg L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
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P4Reg xList,yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
P4Reg equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
P4Reg
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
Param
mode screen
Param
Sets parametric graphing mode.
Pause
program editor
CTL menu
Pause string
Pause value
Pause list
Pause matrix
Pause vector
Displays the specified argument and then suspends
program execution until the user presses b.
Program segment:
©
:Input "Enter x:",x
:y1=x
2
N
6
:Disp "y1 is:",y1
:Pause "Press ENTER to graph"
:ZStd
©
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Pause
Suspends program execution until the user presses
b.
Percent:
%
MATH MISC menu
number%
or
(expression)%
Returns a real
number
or
expression
divided by 100.
5%
b
.05
5%
¹
200
b
10
(10+5)%
¹
200
b
30
pEval(
MATH MISC menu
pEval(coefficientList,xValue)
Returns the value of a polynomial (whose coefficients
are given in
coefficientList
) at
xValue
.
Evaluate y=2x
2
+2x+3 at x=5:
pEval({2,2,3},5)
b
63
PlOff
STAT PLOT menu
PlOff
[
1,2,3
]
Deselects the specified stat plot numbers.
PlOff 1,3
b
Done
PlOff
Deselects all stat plot numbers.
PlOff
b
Done
PlOn
STAT PLOT menu
PlOn
[
1,2,3
]
Selects the specified stat plot numbers, in addition to
any plot numbers that are already selected.
PlOn 2,3
b
Done
PlOn
Selects all stat plot numbers.
PlOn
b
Done
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Plot1(
Plot2(
Plot3(
STAT PLOT menu
The syntax and
descriptions to the right
refer to
Plot1(
, but they
apply as well to
Plot2(
and
Plot3(
.
Scatter plot ®
Plot1(1,
xListName
,
yListName
,
mark
)
Plot1(1,
xListName
,
yListName
)
Defines and selects the plot using real data pairs in
xListName
and
yListName
.
The optional
mark
specifies the character used to plot
the points. If you omit
mark
, a box is used.
mark
:
1
= box (
)
2
= cross (+)
3
= dot (
¦
)
xyLine plot
Plot1(2,
xListName
,
yListName
,
mark
)
Plot1(2,
xListName
,
yListName
)
{
L
9,
L
6,
L
4,
L
1,2,5,7,10}
L1
b
{
L
9
L
6
L
4
L
1 2 5 7 1…
{
L
7,
L
6,
L
2,1,3,6,7,9}
L2
b
{
L
7
L
6
L
2 1 3 6 7 9}
Plot1(1,L1,L2)
b
Done
ZStd
b
Modified box plot ¯
Plot1(3,
xListName
,1
or frequencyListName
,
mark
)
Plot1(3,
xListName
,1
or frequencyListName
)
Plot1(3,
xListName
)
Defines and selects the plot using real data points in
xListName
with the specified frequencies. If you omit
1
or frequencyListName
, frequencies of 1 are used.
Histogram ¬
Plot1(4,
xListName
,1
or frequencyListName
)
Plot1(4,
xListName
)
Box plot °
Plot1(5,
xListName
,1
or frequencyListName
)
Plot1(5,
xListName
)
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Pol
mode screen
Pol
Sets polar graphing mode.
4
Pol
CPLX menu
complexNumber
4
Pol
Displays
complexNumber
in polar form
(
magnitudeangle
), regardless of the complex number
mode.
In
RectC
complex number mode:
L
2
b
(0,1.41421356237)
Ans
4
Pol
b
(1.41421356237
±
1.570…
list
4
Pol
matrix
4
Pol
vector
4
Pol
Returns a list, matrix, or vector in which each element
of the argument is displayed in polar form.
{1,
L
2}
b
{(1,0) (0,1.141421356…
Ans
4
Pol
b
{(1
±
0) (1.4142135623…
PolarC
mode screen
PolarC
Sets polar complex number mode (
magnitudeangle
).
In
PolarC
complex number mode:
L
2
b
(1.41421356237
±
1.570…
Polar complex:
-
magnitude
angle
Used to enter complex numbers in polar form. The
angle
is interpreted according to the current angle
mode.
In
Radian
angle mode and
PolarC
complex
number mode:
(1,2)+(3
p
/4)
b
(5.16990542093
.9226…
PolarGC
graph format screen
PolarGC
Displays graph coordinates in polar form.
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poly
-
v
poly
coefficientList
Returns a list containing the real and complex roots of a
polynomial whose coefficients are given in
coefficientList
.
a
n
x
n
+ ... + a
2
x
2
+ a
1
x
1
+ a
0
x
0
= 0
Find the roots of 2x
3
N
8x
2
N
14x+20=0:
poly {2,
L
8,
L
14,20}
b
{5
L
2 1}
Power:
^
@
number
^
power
or
(
expression
)^(
expression
)
Returns
number
raised to
power
. The arguments can be
real or complex.
4^2
b
16
2^
L
5
b
.03125
listA
^
listB
Returns a list in which each element of
listA
is raised to
the power specified by the corresponding element in
listB
.
{2,3,4}^{3,4,5}
b
{8 81 1024}
squareMatrix
^
power
Returns a matrix equivalent to
squareMatrix
multiplied
by itself
power
number of times, where 0
power
255.
This is not the same as simply raising each element to
power
.
[[2,3][4,5]]^3
b
[[116 153]
[204 269]]
Power of 10:
10
^
-
z
10
^
power
or
10
^(
expression
)
Returns 10 raised to
power
or
expression
, which can be
real or complex.
10
^1.5
b
31.6227766017
10
^
L
2
b
.01
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10
^
list
Returns a list in which each element is 10 raised to the
power specified by the corresponding element in
list
.
10
^{1.5,
L
2}
b
{31.6227766017 .01}
prod
LIST OPS menu
MATH MISC menu
prod
list
Returns the product of all real or complex elements in
list
.
prod {1,2,4,8}
b
64
prod {2,7,
L
8}
b
L
112
Prompt
program editor
I/O menu
(Promp shows on menu)
Prompt
variableA
[
,
variableB
,
...]
Prompts the user to enter a value for
variableA
, then
variableB
, and so on.
Program segment:
©
:Prompt A,B,C
©
PtChg(
GRAPH DRAW menu
PtChg(
x
,
y
)
Reverses the point at graph coordinates (
x
,
y
).
PtChg(
L
6,2)
PtOff(
GRAPH DRAW menu
PtOff(
x
,
y
)
Erases the point at graph coordinates (
x
,
y
).
PtOff(3,5)
PtOn(
GRAPH DRAW menu
PtOn(
x
,
y
)
Draws the point at graph coordinates (
x
,
y
).
PtOn(3,5)
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PwrR
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
PwrR
xList
,
yList
,
frequencyList
,
equationVariable
Fits a power regression model (y=ax
b
) to positive real
data pairs in
xList
and
yList
, using frequencies in
frequencyList
. The regression equation is stored to
equationVariable
, which must be a built-in equation
variable such as
y1
,
r1
, and
xt1
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to built-in variables
xStat
,
yStat
,
and
fStat
, respectively. The regression equation is
stored also to built-in equation variable
RegEq
.
PwrR
xList
,
yList
,
equationVariable
Uses frequencies of 1.
PwrR
xList
,
yList
,
frequencyList
Stores the regression equation to
RegEq
only.
PwrR
xList
,
yList
Uses frequencies of 1, and stores the regression
equation to
RegEq
only.
In
Func
graphing mode:
{1,2,3,4,5,6}
L1
b
{1 2 3 4 5 6}
{1,17,21,52,75,133}
L2
b
{1 17 21 52 75 133}
PwrR L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
PwrR
equationVariable
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs. The regression equation is
stored to
equationVariable
and
RegEq
.
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PwrR
Uses
xStat
,
yStat
, and
fStat
, and stores the regression
equation to
RegEq
only.
PxChg(
GRAPH DRAW menu
PxChg(row,column)
Reverses the pixel at (
row
,
column
), where 0
row
62
and 0
column
126.
PxChg(10,95)
PxOff(
GRAPH DRAW menu
PxOff(row,column)
Erases the pixel at (
row
,
column
), where 0
row
62
and 0
column
126.
PxOff(10,95)
PxOn(
GRAPH DRAW menu
PxOn(row,column)
Draws the pixel at (
row
,
column
), where 0
row
62
and 0
column
126.
PxOn(10,95)
PxTest(
GRAPH DRAW menu
PxTest(row,column)
Returns
1
if the pixel at (
row
,
column
) is on,
0
if it is off;
0
row
62 and 0
column
126.
Assuming the pixel at (10,95) is already on:
PxTest(10,95)
b
1
rAdd(
MATRX OPS menu
rAdd(matrix,rowA,rowB)
Returns a matrix in which
rowA
of a real or complex
matrix
is added to (and stored in)
rowB
.
[[5,3,1][2,0,4][3,
L
1,2]]
MAT
b
[[5 3 1]
[2 0 4]
[3
L
1 2]]
rAdd(MAT,2,3)
b
[[5 3 1]
[2 0 4]
[5
L
1 6]]
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Radian
-
m
Radian
Sets radian angle mode.
In
Radian
angle mode:
sin (
p
/2)
b
1
sin 90
b
.893996663601
Radian entry:
r
MATH ANGLE menu
number
r
or
(
expression
)
r
Designates a real
number
or
expression
as radians,
regardless of the angle mode setting.
In
Degree
angle mode:
cos (
p
/2)
b
.999624216859
cos (
p
/2)
r
b
0
list
r
Designates each element in a real
list
as radians.
cos {
p
/2,
p
}
r
b
{0
L
1}
rand
MATH PROB menu
rand
Returns a random number between 0 and 1.
To control a random number sequence, first store an
integer seed value to
rand
(such as
0
rand
).
You may have different results for the first
two examples:
rand
b
.943597402492
rand
b
.146687829222
0
rand:rand
b
.943597402492
0
rand:rand
b
.943597402492
randBin(
MATH PROB menu
(randBi shows on menu)
randBin(
#ofTrials
,
probabilityOfSuccess
,
#ofSimulations
)
Returns a list of random integers from a binomial
distribution, where
#ofTrials
1 and
0
probabilityOfSuccess
1. The
#ofSimulations
is an
integer
1 that specifies the number of integers
returned in the list.
A seed value stored to
rand
also affects
randBin(.
1
rand:randBin(5,.2,3)
b
{0 3 2}
randBin(
#ofTrials
,
probabilityOfSuccess
)
Returns a single random integer.
0
rand:randBin(5,.2)
b
1
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randInt(
MATH PROB menu
(randIn shows on menu)
randInt(
lower
,
upper
,
#ofTrials
)
Returns a list of random integers bound by the specified
integers,
lower
integer
upper
. The
#ofTrials
is an
integer
1 that specifies the number of integers
returned in the list.
A seed value stored to
rand
also affects
randInt(
.
1
rand:randInt(1,10,3)
b
{8 9 3}
randInt(
lower
,
upper
)
Returns a single random integer.
0
rand:randInt(1,10)
b
10
randM(
MATRX OPS menu
randM(
rows
,
columns
)
Returns a
rows
×
columns
matrix filled with random
one-digit integers (
L
9 to 9).
0
rand:randM(2,3)
b
[[4
L
2 0]
[
L
7 8 8]]
randNorm(
MATH PROB menu
(randN shows on menu)
randNorm(
mean
,
stdDeviation
,
#ofTrials
)
Returns a list of random numbers from a normal
distribution specified by
mean
and
stdDeviation
. The
#ofTrials
is an integer
1 that specifies how many
numbers are returned. Each returned number could be
any real number, but most will be within the interval:
[
meanN
3(
stdDeviation
),
mean
+3(
stdDeviation
)].
A seed value stored to
rand
also affects
randNorm(
.
1
rand:randNorm(0,1,3)
b
{
L
.660585055265
L
1.0…
randNorm(
mean
,
stdDeviation
)
Returns a single random number.
0
rand:randNorm(0,1)
b
L
1.58570962271
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RcGDB
GRAPH menu
RcGDB
graphDataBaseName
Restores all settings stored in
graphDataBaseName
.
For a list of settings, refer to
StGDB
on page 361.
RcPic
GRAPH menu
RcPic
pictureName
Displays the current graph and adds the picture stored
in
pictureName
.
real
CPLX menu
real (
complexNumber
)
Returns the real part of
complexNumber
.
real (
real
,
imaginary
)
returns
real
.
real (
magnitude±angle
)
returns
magnitude
¹
cos
(
angle
).
In
Radian
angle mode:
real (3,4)
b
3
real (3
±
4)
b
L
1.96093086259
real
complexList
real
complexMatrix
real
complexVector
Returns a list, matrix, or vector in which each element
is the real part of the corresponding element in the
argument.
In
Radian
angle mode:
real {
L
2,(3,4),(3
±
4)}
b
{
L
2 3
L
1.96093086259}
4
Rec
CPLX menu
complexNumber
4
Rec
Displays
complexNumber
in rectangular form
(
real
,
imaginary
) regardless of the complex number
mode.
In
PolarC
complex number mode:
L
2
b
(1.41421356237
±
1.570…
Ans
4
Rec
b
(0,1.41421356237)
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complexList
4
Rec
complexMatrix
4
Rec
complexVector
4
Rec
Returns a list, matrix, or vector in which each element
of the argument is displayed in rectangular form.
In
PolarC
complex number mode:
[(3
±p
/6),
L
2]
b
[(3
±
.523598775598) (…
Ans
4
Rec
b
[(2.59807621135,1.5)…
RectC
mode screen
RectC
Sets rectangular complex number mode
(
real
,
imaginary
).
In
RectC
complex number mode:
L
2
b
(0,1.41421356237)
RectGC
graph format screen
RectGC
Displays graph coordinates in rectangular form.
RectV
mode screen
RectV
Sets rectangular vector coordinate mode
[x y z]
.
In
RectV
vector coordinate mode:
3
¹
[4
±
5]
b
[3.40394622556
L
11.5…
ref
MATRX OPS menu
ref
matrix
Returns the row-echelon form of a real or complex
matrix
. The number of columns must be greater than or
equal to the number of rows.
[[4,5,6][7,8,9]]
MAT
b
[[4 5 6]
[7 8 9]]
ref MAT
b
[[1 1.14285714286 1.…
[0 1 2 …
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Repeat
program editor
CTL menu
(Repea shows
on menu)
:Repeat
condition
:
commands-to-repeat
:End
:
commands
Executes
commands-to-repeat
until
condition
is true.
Program segment:
©
:6
N
:1
Fact
:Repeat N<1
: Fact
¹
N
Fact
: N
N
1
N
:End
:Disp "6!=",Fact
©
Return
program editor
CTL menu
(Retur shows
on menu)
Return
In a subroutine, exits the subroutine and returns to the
calling program. In the main program, stops execution
and returns to the home screen.
Program segment in the calling program:
©
:Input "Diameter:",DIAM
:Input "Height:",HT
:AREACIRC
:VOL=AREA
¹
HT
:Disp "Volume =",VOL
©
AREACIRC subroutine program:
PROGRAM:AREACIRC
:RADIUS=DIAM/2
:AREA=
p
¹
RADIUS
2
:Return
RK
graph format screen
(scroll down to
second screen)
RK
In
DifEq
graphing mode, uses an algorithm based on the
Runge-Kutta method to solve differential equations.
Typically,
RK
is more accurate than
Euler
but takes
longer to find the solutions.
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rnorm
MATRX MATH menu
rnorm
matrix
Returns the row norm of a real or complex
matrix
. For
each row,
rnorm
sums the absolute values (magnitudes
of complex elements) of all elements on that row. The
returned value is the largest of the sums.
[[
L
5,6,
L
7][3,3,9][9,
L
9,
L
7]]
MAT
b
[[
L
5 6
L
7]
[3 3 9 ]
[9
L
9
L
7]]
rnorm MAT
b
25
rnorm
vector
Returns the largest absolute value (or magnitude) in a
real or complex
vector
.
rnorm [15,
L
18,7]
b
18
Root:
x
MATH MISC menu
x
th
root
x
number
or
x
th
root
x
(
expression
)
Returns the
x
th
root
of
number
or
expression
. The
arguments can be real or complex.
5
x
32
b
2
x
th
root
x
list
Returns a list in which each element is the
x
th
root
of the
corresponding element in
list
.
5
x
{32,243}
b
{2 3}
x
th
rootList
x
list
Returns a list in which each element is the root
specified by the corresponding elements in
x
th
rootList
and
list
.
{5,2}
x
{32,25)
b
{2 5}
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rotL
BASE BIT menu
rotL
integer
Returns a real
integer
with bits rotated one to the left.
Internally,
integer
is represented as a 16-bit binary
number. When the bits are rotated left, the leftmost bit
rotates to the rightmost bit.
rotL
0000111100001111
Ü
= 0001111000011110
Ü
rotL
is not valid in
Dec
number base mode. To enter
hexadecimal numbers
Õ
through
Ú
, use the
BASE A-F
menu. Do not use 1 to type a letter.
In
Bin
number base mode:
rotL 0000111100001111
b
1111000011110
Ü
Leading zeros are not displayed.
rotR
BASE BIT menu
rotR
integer
Returns a real
integer
with bits rotated one to the right.
Internally,
integer
is represented as a 16-bit binary
number. When the bits are rotated right, the rightmost
bit rotates to the leftmost bit.
rotR
0000111100001111
Ü
= 1000011110000111
Ü
rotR
is not valid in
Dec
number base mode. To enter
hexadecimal numbers
Õ
through
Ú
, use the
BASE A-F
menu. Do not use 1 to type a letter.
In
Bin
number base mode:
rotR 0000111100001111
b
1000011110000111
Ü
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round(
MATH NUM menu
round(
number
,
#ofDecimals
)
round(
number
)
Returns a real or complex
number
rounded to the
specified
#ofDecimals
(0 to 11). If
#ofDecimals
is
omitted,
number
is rounded to 12 decimal places.
round(
p
,4)
b
3.1416
round(
p
/4,4)
b
.7854
round(
p
/4)
b
.785398163397
round(
list
,
#ofDecimals
)
round(
matrix
,
#ofDecimals
)
round(
vector
,
#ofDecimals
)
Returns a list, matrix, or vector in which each element
is the rounded value of the corresponding element in
the argument.
#ofDecimals
is optional.
round({
p
,
2,ln 2},3)
b
{3.142 1.414 .693}
round([[ln 5,ln 3][
p
,e^1]],2)
b
[[1.61 1.1 ]
[3.14 2.72]]
rref
MATRX OPS menu
rref
matrix
Returns the reduced row-echelon form of a real or
complex
matrix
. The number of columns must be
greater than or equal to the number of rows.
[[4,5,6][7,8,9]]
MAT
b
[[4 5 6]
[7 8 9]]
rref MAT
b
[[1 0
L
.999999999999…
[0 1 2 …
rSwap(
MATRX OPS menu
rSwap(
matrix
,
rowA
,
rowB
)
Returns a matrix with
rowA
of a real or complex
matrix
swapped with
rowB
.
[[5,3,1][2,0,4][3,
L
1,2]]
MAT
b
[[5 3 1]
[2 0 4]
[3
L
1 2]]
rSwap(MAT,2,3)
b
[[5 3 1]
[3
L
1 2]
[2 0 4]]
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Scatter
STAT DRAW menu
(Scatte shows
on menu)
Scatter
xList
,
yList
Draws a scatter plot on the current graph, using the real
data pairs in
xList
and
yList
.
Scatter
Uses the data in built-in variables
xStat
and
yStat
. These
variables must contain valid data of the same
dimension; otherwise, an error occurs.
{
L
9,
L
6,
L
4,
L
1,2,5,7,10}
XL
b
{
L
9
L
6
L
4
L
1 2 5 7 1…
{
L
7,
L
6,
L
2,1,3,6,7,9}
YL
b
{
L
7
L
6
L
2 1 3 6 7 9}
ZStd:Scatter XL,YL
b
Sci
mode screen
Sci
Sets scientific notation display mode.
In
Sci
notation mode:
123456789
b
1.23456789
E
8
In
Normal
notation mode:
123456789
b
123456789
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Select(
LIST OPS menu
Select(
xListName
,
yListName
)
If a scatter plot or xyline plot is currently selected and
plotted on the graph screen, you can select a subset
(range) of those data points. The selected data points
are stored to
xListName
and
yListName
.
Select(
xListName
,
yListName
)
displays the current
graph screen and starts an interactive session during
which you select a range of data points.
a. Move the cursor to the leftmost (left bound) point of
the range you want to select and press b.
b. Then move the cursor to the rightmost (right bound)
point of the range you want to select and press
b.
A new stat plot of
xListName
and
yListName
replaces
the plot from which you selected the points.
{
L
9,
L
6,
L
4,
L
1,2,5,7,10}
L1
b
{
L
9
L
6
L
4
L
1 2 5 7 1…
{
L
7,
L
6,
L
2,1,3,6,7,9}
L2
b
{
L
7
L
6
L
2 1 3 6 7 9}
Plot1(1,L1,L2):ZStd
b
After the graph is displayed:
Select(L10,L20)
b
Move the cursor to point (2,3) and press
b
. Then move to (10,9) and press
b
.
L10
b
{2 5 7 10}
L20
b
{3 6 7 9}
Send(
program editor
I/O menu
Send(
listName
)
Sends the contents of
listName
to the CBL or CBR
System.
{1,2,3,4,5}
L1:Send(L1)
b
Done
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seq(
MATH MISC menu
seq(
expression
,
variable
,
begin
,
end
,
step
)
Returns a list containing a sequence of numbers created
by evaluating
expression
from
variable
=
begin
to
variable
=
end
in increments of
step
.
seq(x
2
,x,1,8,2)
b
{1 9 25 49}
seq(
expression
,
variable
,
begin
,
end
)
Uses a
step
of 1.
seq(x
2
,x,1,8)
b
{1 4 9 16 25 36 49 6…
SeqG
graph format screen
SeqG
Sets sequential graphing format, in which selected
functions are plotted one at a time.
SetLEdit
LIST OPS menu
(SetLE shows on menu)
SetLEdit
column1ListName
[
,
...
,
column20ListName
]
Removes all lists from the list editor and then stores one
or more
ListNames
in the specified order, starting with
column 1.
SetLEdit
Removes all lists from the list editor and stores built-in
lists
xStat
,
yStat
, and
fStat
in columns 1 through 3,
respectively.
{1,2,3,4}
L1
b
{1 2 3 4}
{5,6,7,8}
L2
b
{5 6 7 8}
SetLEdit L1,L2
b
Done
The list editor now contains:
352
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Shade(
GRAPH DRAW menu
Shade(
lowerFunc
,
upperFunc
,
xLeft
,
xRight
,
pattern
,
patternRes
)
Draws
lowerFunc
and
upperFunc
in terms of
x
on the
current graph and shades the area bounded by
lowerFunc
,
upperFunc
,
xLeft
, and
xRight
. The shading
style is determined by
pattern
(
1
through
4
) and
patternRes
(
1
through
8
).
pattern
:
1
= vertical (default)
3
= negative-slope 45
¡
2
= horizontal
4
= positive-slope 45
¡
patternRes
(resolution):
1 = every pixel (default) 5 = every 5th pixel
2 = every 2nd pixel 6 = every 6th pixel
3 = every 3rd pixel 7 = every 7th pixel
4 = every 4th pixel 8 = every 8th pixel
Shade(
lowerFunc
,
upperFunc
)
Sets
xLeft
and
xRight
to
xMin
and
xMax
, respectively,
and uses the defaults for
pattern
and
patternRes
.
In
Func
graphing mode:
Shade(x
N
2,x^3
N
8 x,
L
5,1,2,3)
b
ClDrw:Shade(x^3
N
8 x,x
N
2)
b
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shftL
BASE BIT menu
shftL
integer
Returns a real
integer
with bits shifted one to the left.
Internally,
integer
is represented as a 16-bit binary
number. When the bits are shifted left, the leftmost bit is
dropped and 0 is used as the rightmost bit.
shftL
0000111100001111
Ü
= 0001111000011110
Ü
shftL
is not valid in
Dec
number base mode. To enter
hexadecimal numbers
Õ
through
Ú
, use the
BASE A-F
menu. Do not use 1 to type a letter.
In
Bin
number base mode:
shftL 0000111100001111
b
1111000011110
Ü
Leading zeros are not displayed.
shftR
BASE BIT menu
shftR
integer
Returns a real
integer
with bits shifted one to the right.
Internally,
integer
is represented as a 16-bit binary
number. When the bits are shifted right, the rightmost
bit is dropped and 0 is used as the leftmost bit.
shftR
0000111100001111
Ü
= 0000011110000111
Ü
shftR
is not valid in
Dec
number base mode. To enter
hexadecimal numbers
Õ
through
Ú
, use the
BASE A-F
menu. Do not use 1 to type a letter.
In
Bin
number base mode:
shftR 0000111100001111
b
11110000111
Ü
Leading zeros are not displayed.
0
0
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ShwSt
CATALOG
ShwSt
Displays the results of the most recent stat calculation.
sign
MATH NUM menu
sign
number
or
sign (
expression
)
Returns
L
1
if the argument is < 0,
1
if it is > 0, or
0
if it is
= 0. The argument must be real.
sign
L
3.2
b
L
1
sign (6+2
N
8)
b
0
sign
list
Returns a list in which each element is
L
1, 1, or 0 to
indicate the sign of the corresponding element in
list
.
sign {
L
3.2,16.8,6+2
N
8}
b
{
L
1 1 0}
SimulG
graph format screen
SimulG
Sets simultaneous graphing format, in which all selected
functions are plotted at the same time.
simult(
-
u
simult(
squareMatrix
,
vector
)
Returns a vector containing the solutions to a system of
simultaneous linear equations that have the form:
a
1,1
x
1
+ a
1,2
x
2
+ a
1,3
x
3
+ ... = b
1
a
2,1
x
1
+ a
2,2
x
2
+ a
2,3
x
3
+ ... = b
2
a
3,1
x
1
+ a
3,2
x
2
+ a
3,3
x
3
+ ... = b
3
Each row in
squareMatrix
contains the
a
coefficients of
an equation, and
vector
contains the
b
constants.
Solve the following for x and y:
3x
N
4y = 7
x + 6y = 6
[[3,
L
4][1,6]]
MAT
b
[[3
L
4]
[1 6 ]]
[7,6]
VEC
b
[7 6]
simult(MAT,VEC)
b
[3 .5]
The solution is x=3 and y=.5.
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sin
=
sin
angle
or
sin (
expression
)
Returns the sine of
angle
or
expression
, which can be
real or complex.
An angle is interpreted as degrees or radians according
to the current angle mode. In any angle mode, you can
designate an angle as degrees or radians by using the
¡
or
r
designator, respectively, from the
MATH ANGLE
menu.
In
Radian
angle mode:
sin
p
/2
b
0
sin (
p
/2)
b
1
sin 45
¡
b
.707106781187
In
Degree
angle mode:
sin 45
b
.707106781187
sin (
p
/2)
r
b
1
The squareMatrix cannot
have repeated
eigenvalues.
sin
list
Returns a list in which each element is the sine of the
corresponding element in
list
.
sin
squareMatrix
Returns a square matrix that is the matrix sine of
squareMatrix
. The matrix sine corresponds to the result
calculated using power series or Cayley-Hamilton
Theorem techniques. This is
not
the same as simply
calculating the sine of each element.
In
Radian
angle mode:
sin {0,
p
/2,
p
}
b
{0 1 0}
In
Degree
angle mode:
sin {0,30,90}
b
{0 .5 1}
sin
L
1
-
{
sin
L
1
number
or
sin
L
1
(
expression
)
Returns the arcsine of
number
or
expression
, which can
be real or complex.
sin
L
1
list
Returns a list in which each element is the arcsine of the
corresponding element in
list
.
In
Radian
angle mode:
sin
L
1
.5
b
.523598775598
sin
L
1
{0,.5}
b
{0 .523598775598}
In
Degree
angle mode:
sin
L
1
1
b
90
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sinh
MATH HYP menu
sinh
number
or
sinh (
expression
)
Returns the hyperbolic sine of
number
or
expression
,
which can be real or complex.
sinh 1.2
b
1.50946135541
sinh
list
Returns a list in which each element is the hyperbolic
sine of the corresponding element in
list
.
sinh {0,1.2}
b
{0 1.50946135541}
sinh
L
1
MATH HYP menu
sinh
L
1
number
or
sinh
L
1
(
expression
)
Returns the inverse hyperbolic sine of
number
or
expression
, which can be real or complex.
sinh
L
1
1
b
.88137358702
sinh
L
1
list
Returns a list in which each element is the inverse
hyperbolic sine of the corresponding element in
list
.
sinh
L
1
{1,2.1,3}
b
{.88137358702 1.4874…
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SinR
STAT CALC menu
Built-in equation variables
such as
y1
,
r1
, and
xt1
are
case-sensitive. Do not use
Y1
,
R1
, and
XT1
.
If you specify a period, the
TI
-
86 may find a solution
more quickly or it may find
a solution when one would
not have been found
otherwise.
SinR
[
iterations
,
]
xList
,
yList
[
,
period
]
,
equationVariable
Attempts to fit a sinusoidal regression model
(y=a sin(bx+c)+d) to real data pairs in
xList
and
yList
,
using an optional estimated
period
. The regression
equation is stored to
equationVariable
, which must be a
built-in equation variable such as
y1
,
r1
, and
xt1
. The
equation’s coefficients always are stored as a list to
built-in variable
PRegC
.
iterations
is optional; it specifies the maximum number
of times (1 through 16) the TI
-
86 will attempt to find a
solution. If omitted, 8 is used. Typically, larger values
result in better accuracy but longer execution times,
and vice versa.
If you omit the optional
period
, the difference between
values in
xList
should be equal and in sequential order.
If you specify
period
, the differences between x values
can be unequal.
Values used for
xList
and
yList
are stored automatically
to built-in variables
xStat
and
yStat
, respectively. The
regression equation is stored also to built-in equation
variable
RegEq
.
The output of
SinR
is always in radians, regardless of
the angle mode setting.
seq(x,x,1,361,30)
L1
b
{1 31 61 91 121 151 …
{5.5,8,11,13.5,16.5,19,19.5,17,
14.5,12.5,8.5,6.5,5.5}
L2
b
{5.5 8 11 13.5 16.5…
SinR L1,L2,y1
b
Plot1(1,L1,L2)
b
Done
ZData
b
SinR
[
iterations
,
]
xList
,
yList
[
,
period
]
Stores the regression equation to
RegEq
only.
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SinR
[
iterations,
]
equationVariable
Uses
xStat
and
yStat
for
xList
and
yList
, respectively.
These built-in variables must contain valid data of the
same dimension; otherwise, an error occurs. The
regression equation is stored to
equationVariable
and
RegEq
.
SinR
[
iterations
]
Uses
xStat
and
yStat
, and stores the regression equation
to
RegEq
only.
SlpFld
graph format screen
(scroll down to
second screen)
SlpFld
In
DifEq
graphing mode, turns on slope fields. To turn
off direction and slope fields, use
FldOff
.
Solver(
-
t
Solver(equation,variable,guess,{lower,upper})
Solves
equation
for
variable
, given an initial
guess
and
lower
and
upper
bounds within which the solution is
sought.
equation
can be an expression, which is
assumed to equal 0.
Solver(equation,variable,guess)
Uses
L
1
E
99 and 1
E
99 for
upper
and
lower
, respectively.
If y=5, solve x
3
+y
2
=125 for x. You guess the
solution is approximately 4:
5
y
b
5
Solver(x^3+y
2
=125,x,4)
b
Done
x
b
4.64158883361
Solver(equation,variable,{guessLower,guessUpper})
Uses the secant line between
guessLower
and
guessUpper
to start the search.
Solver(
will still search
for a solution outside of this range.
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sortA
LIST OPS menu
SortA
list
Returns a list in which the real or complex elements of
list
are sorted in ascending order.
{5,8,
L
4,0,
L
6}
L1
b
{5 8
L
4 0
L
6}
SortA L1
b
{
L
6
L
4 0 5 8}
sortD
LIST OPS menu
SortD
list
Returns a list in which the real or complex elements of
list
are sorted in descending order.
{5,8,
L
4,0,
L
6}
L1
b
{5 8
L
4 0
L
6}
SortD L1
b
{8 5 0
L
4
L
6}
Sortx
LIST OPS menu
Sortx
xListName
,
yListName
,
frequencyListName
Sortx
xListName
,
yListName
In ascending order of
x
elements, sorts real or complex
x
and
y
data pairs and, optionally, their frequencies in
xListName
,
yListName
, and
frequencyListName
. The
lists’ contents are updated to reflect the changes.
{3,1,2}
XL
b
{3 1 2}
{0,8,
L
4}
YL
b
{0 8
L
4}
Sortx XL,YL
b
Done
XL
b
{1 2 3}
YL
b
{8
L
4 0}
Sortx
Uses built-in variables
xStat
and
yStat
for
xListName
and
yListName
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs.
Sorty
LIST OPS menu
Sorty
xListName
,
yListName
,
frequencyListName
Sorty
xListName
,
yListName
In ascending order of
y
elements, sorts real or complex
x
and
y
data pairs and, optionally, their frequencies in
xListName
,
yListName
, and
frequencyListName
. The
lists’ contents are updated to reflect the changes.
{3,1,2}
XL
b
{3 1 2}
{0,8,
L
4}
YL
b
{0 8
L
4}
Sorty XL,YL
b
Done
YL
b
{
L
4 0 8}
XL
b
{2 3 1}
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Sorty
Uses built-in variables
xStat
and
yStat
for
xListName
and
yListName
, respectively. These built-in variables
must contain valid data of the same dimension;
otherwise, an error occurs.
4
Sph
VECTR OPS menu
vector
4
Sph
Displays a 2- or 3-element
vector
as spherical
coordinates in [
r
q
0] or [
r
q
f
] form,
respectively, even if the display mode is not set for
spherical (
SphereV
).
In
RectV
vector coordinate mode:
[0,
L
1]
4
Sph
b
[1
±
L
1.57079632679
±
1.…
[0,0,
L
1]
4
Sph
b
[1
±
0
±
3.14159265359]
SphereV
-
m
SphereV
Sets spherical vector coordinate mode [
r
q
f
].
In
SphereV
vector coordinate mode:
[1,2]
b
[2.2360679775
±
1.1071…
Square:
2
I
number
2
or
(expression)
2
list
2
squareMatrix
2
Returns a real or complex argument multiplied by itself.
To square a negative number, enclose it in parentheses.
A
squareMatrix
multiplied by itself is not the same as
simply squaring each element.
25
2
b
625
(16+9)
2
b
625
L
2
2
b
L
4
(
L
2)
2
b
4
{
L
2,4,25}
2
b
{4 16 625}
[[2,3][4,5]]
2
b
[[16 21]
[28 37]]
Square root:
-
ˆ
number
or
(
expression)
Returns the square root of
number
or
expression
, which
can be real or complex.
25
b
5
(25+11)
b
6
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list
Returns a list in which element is the square root of the
corresponding element in
list
.
In
RectC
complex number mode:
{
L
2,25}
b
{(0,1.41421356237) (…
St
4
Eq(
STRNG menu
St
4
Eq(
stringVariable
,
equationVariable
)
Converts
stringVariable
to a number, expression, or
equation, and stores it in
equationVariable
.
To convert the string and retain the same variable name,
you can set
equationVariable
equal to
stringVariable
.
"5"
x:6 x
b
ERROR 10 DATA TYPE
"5"
x:St
4
Eq(x,x):6 x
b
30
Program segment:
©
:InpSt "Enter y1(x):",STR
:St
4
Eq(STR,y1)
:Input "Enter x:",x
:Disp "Result is:",y1(x)
©
You cannot store a string directly to a built-in
equation variable.
StGDB
GRAPH menu
StGDB
graphDataBaseName
Creates a graph database (GDB) variable that contains
the current:
Graphing mode, graph format settings, and range
variables.
Functions in the equation editor, whether they are
selected, and their graph styles.
To restore the database and recreate the graph, use
RcGDB
(page 343).
If you use
Input
instead of
InpSt
here,
the entered expression is evaluated a
t
the current value of x and the resul
t
(not the expression) is stored.
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Stop
program editor
CTL menu
Stop
Ends program execution and returns to the home
screen.
Program segment:
©
:Input N
:If N==999
:Stop
©
Store to variable:
X
number
variable
or
(
expression
)
variable
string
variable
list
variable
vector
variable
matrix
variable
Stores the specified argument to
variable
.
10
A:4
¹
A
b
40
"Hello"
STR
b
Hello
{1,2,3}
L1
b
{1 2 3}
[1,2,3]
VEC
b
[1 2 3]
[[1,2,3][4,5,6]]
MAT
b
[[1 2 3]
[4 5 6]]
StPic
GRAPH menu
StPic
pictureName
Stores a picture of the current graph screen to
pictureName
.
StReg(
STAT CALC menu
StReg(
variable
)
Stores the most recently calculated regression equation
to
variable
. This lets you save a regression equation by
storing it to any variable as opposed to a built-in
equation variable.
{1,2,3,4,5}
L1
b
{1 2 3 4 5}
{1,20,55,230,742}
L2
b
{1 20 55 230 742}
ExpR L1,L2:StReg(EQ)
b
Done
8
x
b
8
Rcl EQ
b
.41138948780597
¹
4.7879605684671^x
b
113620.765451
Use N==999,
not N=999.
-
EQ
b
recalls th
e
equation. Then
b
evaluate
s
it at the current value of x.
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String entry:
"
STRNG menu
program editor
I/O menu
"
string
"
Defines a string. When you display a string, it is left-
justified on the screen.
Strings are interpreted as text characters, not numbers.
For example, you cannot perform a calculation with
strings such as "4" or "A¹8". To convert between string
variables and equation variables, use
Eq
4
St(
and
St
4
Eq(
as described on pages 290 and 361, respectively.
"Hello"
STR
b
Hello
Disp STR+", Jan"
b
Hello, Jan
Done
sub(
STRNG menu
sub(
string
,
begin
,
length
)
Returns a new string that is a subset of
string
, starting
at character number
begin
and continuing for the
specified
length
.
"The answer is:"
STR
b
The answer is:
sub(STR,5,6)
b
answer
Subtraction:
N
T
numberA
N
numberB
Returns the value of
numberB
subtracted from
numberA
. The arguments can be real or complex.
6
N
2
b
4
10
NL
4.5
b
14.5
list
N
number
Returns a list in which
number
is subtracted from each
element of
list
. The arguments can be real or complex.
{10,9,8}
N
4
b
{6 5 4}
In
RectC
complex number mode:
{8,1,(5,2)}
N
3
b
{(5,0) (
L
2,0) (2,2)}
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listA
N
listB
matrixA
N
matrixB
vectorA
N
vectorB
Returns a list, matrix, or vector that is the result of each
element in the second argument subtracted from the
corresponding element in the first argument. The two
real or complex arguments must have the same
dimension.
{5,7,9}
N
{4,5,6}
b
{1 2 3}
[[5,7,9][11,13,15]]
N
[[4,5,6][7,8,
9]]
b
[[1 2 3]
[4 5 6]]
[5,7,9]
N
[1,2,3]
b
[4 5 6]
sum
MATH MISC menu
LIST OPS menu
sum
list
Returns the sum of all real or complex elements in
list
.
sum {1,2,4,8}
b
15
sum {2,7,
L
8,0}
b
1
tan
?
tan
angle
or
tan (
expression
)
Returns the tangent of
angle
or
expression
, which can
be real or complex.
An angle is interpreted as degrees or radians according
to the current angle mode. In any angle mode, you can
designate an angle as degrees or radians by using the
¡
or
r
designator, respectively, from the
MATH ANGLE
menu.
In
Radian
angle mode:
tan
p
/4
b
0
tan (
p
/4)
b
1
tan 45
¡
b
1
In
Degree
angle mode:
tan 45
b
1
tan (
p
/4)
r
b
1
tan
list
Returns a list in which each element is the tangent of
the corresponding element in
list
.
In
Degree
angle mode:
tan {0,45,60}
b
{0 1 1.73205080757}
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tan
L
1
-
}
tan
L
1
number
or
tan
L
1
(
expression
)
Returns the arctangent of
number
or
expression
, which
can be real or complex.
In
Radian
angle mode:
tan
L
1
.5
b
.463647609001
In
Degree
angle mode:
tan
L
1
1
b
45
tan
L
1
list
Returns a list in which each element is the arctangent of
the corresponding element in
list
.
In
Radian
angle mode:
tan
L
1
{0,.2,.5}
b
{0 .19739555985 .463…
tanh
MATH HYP menu
tanh
number
or
tanh (
expression
)
Returns the hyperbolic tangent of
number
or
expression
, which can be real or complex.
tanh 1.2
b
.833654607012
tanh
list
Returns a list in which each element is the hyperbolic
tangent of the corresponding element in
list
.
tanh {0,1.2}
b
{0 .833654607012}
tanh
L
1
MATH HYP menu
tanh
L
1
number
or
tanh
L
1
(
expression
)
Returns the inverse hyperbolic tangent of
number
or
expression
, which can be real or complex.
tanh
L
1
0
b
0
tanh
L
1
list
Returns a list in which each element is the inverse
hyperbolic tangent of the corresponding element in
list
.
In
RectC
complex number mode:
tanh
L
1
{0,2.1}
b
{(0,0) (.51804596584…
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TanLn(
GRAPH DRAW menu
TanLn(
expression
,
xValue
)
Draws
expression
on the current graph and then draws
a tangent line at
xValue
.
In
Func
graphing mode and
Radian
angle
mode:
ZTrig:TanLn(cos x,
p
/4)
b
Text(
GRAPH DRAW menu
Text(
row
,
column
,
string
)
Writes a text
string
on the current graph beginning at
pixel (
row
,
column
), where 0
row
57 and
0
column
123.
Text at the bottom of the graph may be covered by a
displayed menu. To remove the menu, press :.
Program segment in
Func
graphing mode and
a
ZStd
graph screen:
©
:y1=x sin x
:Text(0,70,"y1=x sin x")
©
When executed:
Then
program editor
CTL menu
Refer to syntax information for
If
, beginning on page 305. See
the
If:Then:End
and
If:Then:Else:End
syntax.
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Trace
GRAPH menu
Trace
Displays the current graph and lets the user trace a
function. From a program, press b to stop tracing
and continue with the program.
Transpose:
T
MATRX MATH menu
matrix
T
Returns a transposed real or complex matrix in which
element
row
,
column
is swapped with element
column
,
row
of
matrix
. For example:
ã
a b
c d
ä
T
returns
ã
a c
b d
ä
For complex matrices, the complex conjugate of each
element is taken.
[[1,2][3,4]]
MATA
b
[[1 2]
[3 4]]
MATA
T
b
[[1 3]
[2 4]]
[[1,2,3][4,5,6][7,8,9]]
MATB
b
[[1 2 3]
[4 5 6]
[7 8 9]]
MATB
T
b
[[1 4 7]
[2 5 8]
[3 6 9]]
In
RectC
complex number mode:
[[(1,2),(1,1)][(3,2),(4,3)]]
MATC
b
[[(1,2) (1,1)]
[(3,2) (4,3)]]
MATC
T
b
[[(1,
L
2) (3,
L
2)]
[(1,
L
1) (4,
L
3)]]
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TwoVar
STAT CALC menu
(TwoVa shows on menu)
TwoVar
xList
,
yList
,
frequencyList
Performs two-variable statistical analysis on the real
data pairs in
xList
and
yList
, using the frequencies in
frequencyList
.
Values used for
xList
,
yList
, and
frequencyList
are
stored automatically to the built-in variables
xStat
,
yStat
, and
fStat
, respectively.
TwoVar
xList
,
yList
Uses frequencies of 1.
TwoVar
Uses
xStat
,
yStat
, and
fStat
for
xList
,
yList
, and
frequencyList
. These built-in variables must contain
valid data of the same dimension; otherwise, an error
occurs.
{0,1,2,3,4,5,6}
L1
b
{0 1 2 3 4 5 6}
{0,1,2,3,4,5,6}
L2
b
{0 1 2 3 4 5 6}
TwoVar L1,L2
b
Scroll down to see more results.
unitV
VECTR MATH menu
unitV
vector
Returns a unit vector of a real or complex
vector
, where:
unitV [a,b,c]
returns [
a
norm
b
norm
c
norm
]
and
norm
is (
a
2
+
b
2
+
c
2
).
In
RectV
vector coordinate mode:
unitV [1,2,1]
b
[.408248290464 .8164…
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vc
4
li
LIST OPS menu
VECTR OPS menu
vc
4
li
vector
Returns a real or complex
vector
converted to a list.
vc
4
li [2,7,
L
8,0]
b
{2 7
L
8 0}
(vc
4
li [2,7,
L
8,0])
2
b
{4 49 64 0}
Vector entry:
[ ]
-
and
-
[
element1
,
element2
,
...
]
Defines a vector in which each element is a real or
complex number or variable.
[4,5,6]
VEC
b
[4 5 6]
In
PolarC
complex number mode:
[5,(2
±p
/4)]
VEC
b
[(5
±
0) (2
±
.785398163…
Vert
GRAPH DRAW menu
Vert
xValue
Draws a vertical line on the current graph at
xValue
.
In a
ZStd
graph screen:
Vert
L
4.5
b
While
program editor
CTL menu
:While
condition
:
commands-while-true
:End
:
command
Executes
commands-while-true
as long as
condition
is
true.
Program segment:
©
:1
J
:0
TEMP
:While J
20
: TEMP+1/J
TEMP
: J+1
J
:End
:Disp "Reciprocal sums to
20",TEMP
©
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xor
BASE BOOL menu
integerA
xor
integerB
Compares two real integers bit by bit. Internally, both
integers are converted to binary. When corresponding
bits are compared, the result is 1 if either bit (but not
both) is 1; the result is 0 if both bits are 0 or both bits
are 1. The returned value is the sum of the bit results.
For example, 78
xor
23 = 89.
78 = 1001110
Ü
23 = 0010111
Ü
1011001
Ü
=89
You can enter real numbers instead of integers, but they
are truncated automatically before the comparison.
In
Dec
number base mode:
78 xor 23
b
89
In
Bin
number base mode:
1001110 xor 10111
b
1011001
Ü
Ans
4
Dec
b
89
Þ
xyline
STAT DRAW menu
xyline
xList
,
yList
Draws a line plot on the current graph, using the real
data pairs in
xList
and
yList
.
xyline
Uses the data in built-in variables
xStat
and
yStat
. These
variables must contain valid data of the same
dimension; otherwise, an error occurs.
{
L
9,
L
6,
L
4,
L
1,2,5,7,10}
XL
b
{
L
9
L
6
L
4
L
1 2 5 7 1…
{
L
7,
L
6,
L
2,1,3,6,7,9}
YL
b
{
L
7
L
6
L
2 1 3 6 7 9}
ZStd:xyline XL,YL
b
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ZData
GRAPH ZOOM menu
ZData
Adjusts the window variable values based on the
currently defined statistical plots so that all stat data
points will be plotted, and then updates the graph
screen.
In
Func
graphing mode:
{1,2,3,4}
XL
b
{1 2 3 4}
{2,3,4,5}
YL
b
{2 3 4 5}
Plot1(1,XL,YL)
b
Done
ZStd
b
ZData
b
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ZDecm
GRAPH ZOOM menu
ZDecm
Sets the window variable values such that
@
x
=
@
y
=.
1
,
and then updates the graph screen with the origin
centered on the screen.
xMin=
L
6.3 yMin=
L
3.1
xMax=6.3 yMax=3.1
xScl=1 yScl=1
One of the benefits of
ZDecm
is that you can trace in .1
increments.
In
Func
graphing mode:
y1=x sin x
b
Done
ZStd
b
If you trace the graph above,
x
values start at 0
and increment by .1587301587.
ZDecm
b
If you trace this graph, the
x
values increment
by .1.
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ZFit
GRAPH ZOOM menu
ZFit
Recalculates
yMin
and
yMax
to include the minimum
and maximum
y
values of the selected functions
between the current
xMin
and
xMax
, and then updates
the graph screen.
This does not affect
xMin
and
xMax
.
In
Func
graphing mode:
y1=x
2
N
20
b
Done
ZStd
b
ZFit
b
ZIn
GRAPH ZOOM menu
ZIn
Zooms in on the part of the graph centered around the
current cursor location.
Zoom factors are set by the values of built-in variables
xFact
and
yFact
; the default is 4 for both factors.
In
Func
graphing mode:
y1=x sin x
b
Done
ZStd
b
ZIn
b
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ZInt
GRAPH ZOOM menu
ZInt
Sets the window variable values so that each pixel is an
integer in all directions (
@
x
=
@
y
=
1
), sets
xScl
=
yScl
=
10
,
and then updates the graph screen.
The current cursor location becomes the center of the
new graph.
One of the benefits of
ZInt
is that you can trace in whole
number increments.
In
Func
graphing mode:
y1=der1(x
2
N
20,x)
b
Done
ZStd
b
If you trace the graph above,
x
values start at 0
and increment by .1587301587.
ZInt
b
If you trace this graph,
x
values increment
by 1.
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ZOut
GRAPH ZOOM menu
ZOut
Zooms out to display more of the graph, centered
around the current cursor location.
Zoom factors are set by the values of built-in variables
xFact
and
yFact
; the default is 4 for both factors.
In
Func
graphing mode:
y1=x sin x
b
Done
ZStd
b
ZOut
b
ZPrev
GRAPH ZOOM menu
ZPrev
Replots the graph using the window variable values of
the graph that was displayed before you executed the
previous
ZOOM
instruction.
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ZRcl
GRAPH ZOOM menu
ZRcl
Sets the window variables to values stored previously in
the user-defined zoom-window variables, and then
updates the graph screen.
To set user-defined zoom-window variables, either:
Press 6 ( / / / & (
ZSTO
) to
store the current graph’s window variables.
– or –
Store the applicable values to the zoom-window
variables, whose names begin with
z
followed by the
regular window variable name. For example, store a
value for xMin to
zxMin
, yMin to
zyMin
, etc.
ZSqr
GRAPH ZOOM menu
ZSqr
Sets the window variable values to produce “square”
pixels where
@
x
=
@
y
, and then updates the graph screen.
The center of the current graph (not necessarily the
axes intersection) becomes the center of the new graph.
In other types of zooms, squares may look like
rectangles and circles may look like ovals. Use
ZSqr
for
a more accurate shape.
In
Func
graphing mode:
y1=
(8
2
N
x
2
):y2=
L
y1
b
Done
ZStd
b
ZSqr
b
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ZStd
GRAPH ZOOM menu
ZStd
Sets the window variables to the standard default
values, and then updates the graph screen.
Func
graphing mode:
xMin=
L
10 yMin=
L
10
xMax=10 yMax=10
xScl=1 yScl=1
Pol
graphing mode:
q
Min=0 xMin=
L
10 yMin=
L
10
q
Max=6.28318530718 (2
p
) xMax=10 yMax=10
q
Step=.130899693899… (
p
/24) xScl=1 yScl=1
Param
graphing mode:
tMin=0 xMin=
L
10 yMin=
L
10
tMax=6.28318530718 (2
p
) xMax=10 yMax=10
tStep=.130899693899… (
p
/24) xScl=1 yScl=1
DifEq
graphing mode:
tMin=0 xMin=
L
10 yMin=
L
10
tMax=6.28318530718 (2
p
) xMax=10 yMax=10
tStep=.130899693899… (
p
/24) xScl=1 yScl=1
tPlot=0 difTol=.001
In
Func
graphing mode:
y1=x sin x
b
Done
ZStd
b
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ZTrig
GRAPH ZOOM menu
ZTrig
Sets the window variables to preset values appropriate
for plotting trig functions in
Radian
angle mode
(
@
x
=
p
/24), and then updates the graph screen.
xMin=
L
8.24668071567 yMin=
L
4
xMax=8.24668071567 yMax=4
xScl=1.5707963267949 (
p
/2) yScl=1
In
Func
graphing mode:
y1=sin x
b
Done
ZStd
b
ZTrig
b
379
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TI
-
86 Menu Map.............................................................. 380
Handling a Difficulty ........................................................ 392
Error Conditions............................................................... 393
Equation Operating System (EOS
é
) ................................397
TOL (The Tolerance Editor)
-
)
................... 398
Computational Accuracy.................................................. 399
Support and Service Information ..................................... 400
Warranty Information ......................................................402
F1 F2 F3
F4
F5
M1 M2
M3
M4
M5
TI 86
-
Appendix
A
380
Appendix
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TI-86 Menu Map
This section presents the TI
-
86 menus as they appear on the TI
-
86 keyboard, starting at the
top. If a menu has items that display other menus, the other menus follow directly below
the main menu. In the program editor, the appearance of some menus changes slightly. The
menu map omits user-created-name menus, such as the
LIST
NAMES
and
CONS
USER
menus.
LINK Menu
-
o
SEND RECV SND85
LINK SEND Menu
-
o
&
BCKUP PRGM MATRX GDB ALL
4
LIST VECTR REAL CPLX EQU
4
CONS PIC WIND STRNG
SEND BCKUP Menu
-
o
&
&
XMIT
LINK SEND Selection Screen Menu
-
o
&
data type
XMIT SELCT ALL+ ALL
N
LINK SND85 Menu
-
o
(
MATRX LIST VECTR REAL CPLX
4
CONS PIC STRNG
GRAPH Menu
6
in Func graphing mode
y(x)= WIND ZOOM TRACE GRAPH
4
MATH DRAW FORMT STGDB RCGDB
4
EVAL STPIC RCPIC
The link menus are not
available in the program
editor.
In the program editor,
DrEqu
is available as a
GRAPH
menu item.
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381
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GRAPH Menu
6
in Pol graphing mode
r(
q
)= WIND ZOOM TRACE GRAPH
4
MATH DRAW FORMT STGDB RCGDB
4
EVAL STPIC RCPIC
GRAPH Menu
6
in Param graphing mode
E(t)= WIND ZOOM TRACE GRAPH
4
MATH DRAW FORMT STGDB RCGDB
4
EVAL STPIC RCPIC
GRAPH Menu
6
in DifEq graphing mode
Q'(t)= WIND INITC AXES GRAPH
4
FORMT DRAW ZOOM TRACE EXPLR
4
EVAL STGDB RCGDB STPIC RCPIC
Equation Editor Menu
6
&
in Func graphing mode
y(x)= WIND ZOOM TRACE GRAPH
x y INSf DELf SELCT
4
ALL+ ALL
N
STYLE
Equation Editor Menu
6
&
in Pol graphing mode
r(
q
)= WIND ZOOM TRACE GRAPH
q
r INSf DELf SELCT
4
ALL+ ALL
N
STYLE
Equation Editor Menu
6
&
in Param graphing mode
E(t)= WIND ZOOM TRACE GRAPH
t xt yt DELf SELCT
4
INSf ALL+ ALL
N
STYLE
Equation Editor Menu
6
&
in DifEq graphing mode
Q'(t)= WIND INITC AXES GRAPH
t Q INSf DELf SELCT
4
ALL+ ALL
N
STYLE
382
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GRAPH VARS (Graph Variables) Menu
6
&
in the program editor only
y(x)= WIND ZOOM TRACE GRAPH
y x xt yt t
4
r
q
Q1 Q'1 t
4
FnOn FnOff Axes Q
[
dTime
4
fldRes
GRAPH WIND (Window Variables) Menu
6
'
in the program editor only
y(x)= WIND ZOOM TRACE GRAPH
xMin xMax xScl yMin yMax
4
yScl tMin tMax tStep
q
Min
4q
Max
q
Step tPlot difTol xRes
4
EStep
GRAPH ZOOM Menu
6
(
y(x)= WIND ZOOM TRACE GRAPH
BOX ZIN ZOUT ZSTD ZPREV
4
ZFIT ZSQR ZTRIG ZDECM ZDATA
4
ZRCL ZFACT ZOOMX ZOOMY ZINT
4
ZSTO
GRAPH MATH Menu
6
/
&
in Func graphing mode
MATH DRAW FORMT STGDB RCGDB
ROOT dy
à
dx
f(X) FMIN FMAX
4
INFLC YICPT ISECT DIST ARC
4
TANLN
GRAPH MATH Menu
6
/
&
in Pol graphing mode
MATH DRAW FORMT STGDB RCGDB
DIST dy
à
dx dr
à
d
q
ARC TANLN
To display the
GRAPH
ZOOM
menu in
DifEq
mode, press
6
/
(
.
DifEq
graphing mode has no
GRAPH
MATH
menu.
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GRAPH MATH Menu
6
/
&
in Param graphing mode
MATH DRAW FORMT STGDB RCGDB
DIST dy
à
dx dy
à
dt dx
à
dt ARC
4
TANLN
GRAPH DRAW Menu
6
/
'
MATH DRAW FORMT STGDB RCGDB
Shade LINE VERT HORIZ CIRCL
4
DrawF PEN PTON PTOFF PTCHG
4
CLDR
W
PxOn PxOff PxChg PxTest
4
TEXT TanLn DrInv
SOLVER Menu
-
t
equation
b
SOLVER ZOOM Menu
-
t
equation
b
(
GRAPH WIND ZOMM TRACE SOLVE BOX ZINT ZOUT ZFACT ZSTD
TABLE Menu
7
TABLE SETUP Menu
7
'
TABLE TBLST TABLE
Table Screen Menu
7
&
in Func graphing mode in Param graphing mode
TBLST SELCT x y TBLST SELCT t xt yt
in Pol graphing mode in DifEq graphing mode
TBLST SELCT
q
r TBLST SELCT t Q
SIMULT ENTRY Menu
-
u
(integer
2 &
30)
b
SIMULT RESULT Menu
*
PREV NEXT CLRq SOLVE COEFS STOa STOb STOx
DrInv
is available only in
Func graphing mode.
DrEqu
is available only in
DifEq
graphing mode.
384
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PRGM Menu
8
NAMES EDIT
Program Editor Menu
8
'
program name
b
PAGE
$
PAGE
#
I
à
O CTL INSc
4
DELc UNDEL :
PRGM I
à
O (Input
à
Output) Menu
8
'
program name
b
(
PAGE
$
PAGE
#
I
à
O CTL INSc
Input Promp Disp DispG DispT
4
ClTbl Get Send getKy ClLCD
4
" Outpt InpSt
PRGM CTL (Control) Menu
8
'
programName
b
)
PAGE
$
PAGE
#
I
à
O CTL INSc
If Then Else For End
4
While Repea Menu Lbl Goto
4
IS> DS< Pause Retur Stop
4
DelVa GrStl LCust
POLY ENTRY Menu
-
v
(integer
2 &
30)
b
POLY RESULT Menu
*
CLRq SOLVE COEFS STOa
CUSTOM Menu
9
44
CATLG-VARS Menu
-
w
CATLG ALL REAL CPLX LIST
4
VECTR MATRX STRNG EQU CONS
4
PRGM GDB PIC STAT WIND
CATLG-VARS Selection Menu
-
w
&
or select a data type
PAGE
$
PAGE
#
CUSTM BLANK
Use the
CUSTOM
menu to
create your own menu
(Chapter 2).
Appendix
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CALC Menu
-
evalF nDer der1 der2 fnInt
4
fMin fMax arc
MATRX Menu
-
Matrix Editor Menu
-
'
matrixName
b
NAMES EDIT MATH OPS CPLX INSr DELr INSc DELc
4
REAL
MATRX MATH Menu
-
(
NAMES EDIT MATH OPS CPLX
det
T
norm eigVl eigVc
4
rnorm cnorm LU cond
MATRX OPS (Operations) Menu
-
)
NAMES EDIT MATH OPS CPLX
dim Fill ident ref rref
4
aug rSwap rAdd multR mRAdd
4
randM
MATRX CPLX Menu
-
*
NAMES EDIT MATH OPS CPLX
conj real imag abs angle
VECTR Menu
-
Š
Vector Editor Menu
-
Š
'
vectorName
b
NAMES EDIT MATH OPS CPLX INSi DELi
4
REAL
VECTR MATH Menu
-
Š
(
NAMES EDIT MATH OPS CPLX
cross unitV norm dot
386
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VECTR OPS (Operations) Menu
-
Š
)
NAMES EDIT MATH OPS CPLX
dim Fill
4
Pol
4
Cyl
4
Sph
44
Rec li
4
vc vc
4
li
VECTR CPLX Menu
-
Š
*
NAMES EDIT MATH OPS CPLX
conj real imag abs angle
CPLX (Complex Number) Menu
-
conj real imag abs angle
44
Rec
4
Pol
MATH Menu
-
Œ
NUM PROB ANGLE HYP MISC
4
INTER
MATH NUM (Number) Menu
-
Œ
&
NUM PROB ANGLE HYP MISC
round iPart fPart int abs
4
sign min max mod
MATH PROB (Probability) Menu
-
Œ
'
NUM PROB ANGLE HYP MISC
! nPr nCr rand randln
4
randN randBi
MATH ANGLE Menu
-
Œ
(
NUM PROB ANGLE HYP MISC
¡
r
'
4
DMS
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MATH HYP (Hyperbolic) Menu
-
Œ
)
NUM PROB ANGLE HYP MISC
sinh cosh tanh sinh
L
1
cosh
L
1
4
tanh
L
1
MATH MISC (Miscellaneous) Menu
-
Œ
*
NUM PROB ANGLE HYP MISC
sum prod seq lcm gcd
44
Frac % pEval x
eval
CONS (Constants) Menu
-
BLTIN EDIT USER
CONS BLTIN (Built-In Constants) Menu
-
&
BLTIN EDIT USER
Na k Cc ec Rc
4
Gc g Me Mp Mn
4m
0
H
0h c u
CONV (Conversions) Menu
-
LNGTH AREA VOL TIME TEMP
4
MASS FORCE PRESS ENRGYPOWE
R
4
SPEED
CONV LNGTH (Length) Menu
-
&
LNGTH AREA VOL TIME TEMP
mm cm m in ft
4
yd km mile nmile lt-yr
4
mil Ang fermi rod fath
CONV AREA Menu
-
'
LNGTH AREA VOL TIME TEMP
ft
2
m
2
mi
2
km
2
acre
4
in
2
cm
2
yd
2
ha
388
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CONV VOL (Volume) Menu
-
(
LNGTH AREA VOL TIME TEMP
liter gal qt pt oz
4
cm
3
in
3
ft
3
m
3
cup
4
tsp tbsp ml galUK ozUK
CONV TIME Menu
-
)
LNGTH AREA VOL TIME TEMP
sec mn hr day yr
4
week ms
µ
sns
CONV TEMP (Temperature) Menu
-
*
LNGTH AREA VOL TIME TEMP
¡
C
¡
F
¡
K
¡
R
CONV MASS Menu
-
/
&
MASS FORCE PRESS ENRGY POWE
R
gm kg lb amu slug
4
ton mton
CONV FORCE Menu
-
/
'
MASS FORCE PRESS ENRGYPOWE
R
N dyne tonf kgf lbf
CONV PRESS (Pressure) Menu
-
/
(
MASS FORCE PRESS ENRGY POWE
R
atm bar N
à
m
2
lb
à
in
2
mmHg
4
mmH
2
inHg inH
2
0
CONV ENRGY (Energy) Menu
-
/
)
MASS FORCE PRESS ENRGY POWE
R
J cal Btu ft-lb kw-hr
4
eV erg I-atm
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CONV POWER Menu
-
/
*
CONV SPEED Menu
-
/
/
&
MASS FORCE PRESS ENRGYPOWE
R
SPEED
hp W ftlb
à
s cal
à
s Btu
à
mft
à
sm
à
smi
à
hr km
à
hr knot
STRNG Menu
-
" sub lngth Eq
4
St St
4
Eq
LIST Menu
-
LIST NAMES Menu
-
(
{ } NAMES EDIT OPS { } NAMES EDIT OPS
fStat xStat yStat
List Editor Menu
-
)
{ } NAMES " OPS
44
REAL
LIST OPS (Operations) Menu
-
*
{ } NAMES EDIT OPS
dimL sortA sortD min max
4
sum prod seq li
4
vc vc
4
li
4
Fill aug cSum Deltal Sortx
4
Sorty Select SetLE Form
The (Number) BASE Menu
-
BASE
Õ
-
Ú
(Hexadecimal) Menu
-
&
Õ
-
Ú
TYPE CONV BOOL BIT
Õ
TYPE CONV BOOL BIT
Ö×ØÙÚ
BASE TYPE Menu
-
'
BASE CONV (Conversions) Menu
-
(
Õ
-
Ú
TYPE CONV BOOL BIT
Õ
-
Ú
TYPE CONV BOOL BIT
ÜßÝÞ
4
Bin
4
Hex
4
Oct
4
Dec
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BASE BOOL (Boolean) Menu
-
)
BASE BIT Menu
-
*
Õ
-
Ú
TYPE CONV BOOL BIT
Õ
-
Ú
TYPE CONV BOOL BIT
and or xor not rotR rotL shftR shftL
TEST (Relational) Menu
-
˜
== < >
‚4ƒ
MEM (Memory) Menu
-
RAM DELET RESET TOL ClrEnt
MEM DELET (Delete) Menu
-
'
ALL REAL CPLX LIST VECTR
4
MATRX STRNG EQU CONS PRGM
4
GDB PIC
MEM RESET Menu
-
(
MEM RESET Are You Sure? Menu
RAM DELET RESET TOL ClrEnt YES NO
ALL MEM DFLTS
STAT (Statistics) Menu
-
š
CALC EDIT PLOT DRAW VARS
4
FCST
STAT CALC (Calculations) Menu
-
š
&
CALC EDIT PLOT DRAW VARS
OneVa TwoVa LinR LnR ExpR
4
PwrR SinR LgstR P2Reg P3Reg
4
P4Reg StReg
When you press
-
š
'
, the list editor and list
menu are displayed.
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STAT PLOT Menu
-
š
(
Plot Type Menu
-
š
(
(
&
,
'
, or
(
)
#
PLOT1 PLOT2 PLOT3 PlOn PlOff PLOT1 PLOT2 PLOT3 PlOn PlOff
SCAT xyLINE MBOX HIST BOX
Plot Mark Menu
-
š
(
(
&
,
'
, or
(
)
#
(
&
,
'
, or
(
)
#
#
#
PLOT1 PLOT2 PLOT3 PlOn PlOff
+
¦
STAT DRAW Menu
-
š
)
CALC EDIT PLOT DRAW VARS
HIST SCAT xyLINE BOX MBOX
4
DRREG CLDR
W
DrawF STPIC RCPIC
STAT VARS (Statistical Result Variables) Menu
-
š
*
CALC EDIT PLOT DRAW VARS
vs
xSx
ws
y
4
Sy
G
x
G
x
2
G
y
G
y
2
4G
xy RegEq corr a b
4
n minX maxX minY maxY
4
Med PRegC Qrtl1 Qrtl3 tolMe
CHAR (Character) Menu
-
Ÿ
MISC GREEK INTL
CHAR MISC (Miscellaneous) Menu
-
Ÿ
&
MISC GREEK INTL
?#&%'
4
!@$~|
4
¿ÑñÇç
Ñ
,
ñ
,
Ç
, and
ç
are valid as the
first letter of a variable name.
%
,
'
, and
!
can be functions.
392
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CHAR GREEK Menu
-
Ÿ
'
MISC GREEK INTL
abg@d4Hqlmr
4G s
ι
fJ
CHAR INTL (International Letter Symbols) Menu
-
Ÿ
(
MISC GREEK INTL
´`^¨
Handling a Difficulty
If you cannot see anything on the screen, you may need to adjust the contrast (Chapter 1).
To darken the screen, press and release -, and then press and hold $.
To lighten the screen, press and release -, and then press and hold #.
If an error menu is displayed, follow the steps in Chapter 1. Refer to the Error Conditions section
of the Appendix (page 393) for details about specific errors, if necessary.
If a checkerboard cursor ( Ä ) is displayed, then either you have entered the maximum number
of characters in a prompt or memory is full. If memory is full, press - ', select a data
type, and then delete some items from memory (Chapter 17).
If the busy indicator (dotted line) is displayed in the top-right corner, a graph or program has
paused; the TI
-
86 is waiting for input. Press b to continue or press ^ to break.
If the calculator does not seem to work at all, be sure the batteries are fresh and that they are
installed properly. Refer to battery information in Chapter 1.
All
CHAR
GREEK
menu items
are valid variable-name
characters, including the first
letter.
p
(
-
~
)
is not valid
as a character;
p
is a
constant on the TI
-
86.
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Error Conditions
When the TI
-
86 detects an error, it displays an error message
ERROR
#
type
and the error menu.
Chapter 1 describes how to correct an error. This section describes possible causes for the
errors and examples. To find the proper arguments for a function or instruction, as well as
restrictions on those arguments, refer to Chapter 20: A to Z Function and Instruction Reference.
01 OVERFLOW
You attempted to enter a number that is beyond the calculator’s range.
You attempted to execute an expression with a result that is beyond the
calculator’s range.
02 DIV BY ZERO
You attempted to divide by zero.
You attempted a linear regression with a vertical line.
03 SINGULAR MAT
You attempted to use a singular matrix (determinate = 0) as the argument
for
L
1
,
Simult
, or
LU
.
You attempted a regression with at least one inappropriate list.
You attempted to use a matrix with repeated eigenvalues as the argument
for
exp
,
cos
, or
sin
.
04 DOMAIN
You attempted to use an argument that is out of the range of valid values
for the function or instruction.
You attempted a logarithmic or power regression with a
L
x or an
exponential regression with a
L
y.
05 INCREMENT
The increment in
seq
is
0
or has the wrong sign; the increment for a loop is
0
.
06 BREAK
You pressed
^
to break a program,
DRAW
instruction, or expression evaluation.
07 SYNTAX
You entered a value; look for misplaced functions, arguments, parentheses, or
commas; check the syntax description in the A to Z Reference.
Errors 1 through 5 do not
occur during graphing. The
TI
-
86 allows for undefined
values on a graph.
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08 NUMBER BASE
You entered an invalid digit in a number base, such as
7
Ü.
You attempted an operation that is not allowed in
Bin
,
Oct
, or
Hex
base mode.
09 MODE
You attempted to store to a window variable of a noncurrent graphing mode.
or to use an instruction valid only in noncurrent graphing modes; for example,
using
DrInv
in
Pol
,
Param
, or
DifEq
graphing mode.
10 DATA TYPE
You entered a value or variable that is an inappropriate data type.
You entered an argument that is an inappropriate data type for a function
or an instruction, such as a program name for
sortA
.
In an editor, you entered a data type that is not allowed; check the
appropriate chapter.
You attempted to store data to a protected data type, such as a constant,
program, picture, or graph database.
You attempted to store inappropriate data to a restricted built-in variable,
such as the list names
xStat
,
yStat
, and
fStat
.
11 ARGUMENT
You attempted to execute a function or instruction without all the arguments.
12 DIM MISMATCH
You attempted to use two or more lists, matrices, or vectors as arguments, but
the dimensions of all arguments are not equal, such as
{1,2}+{1,2,3}
.
13 DIMENSION
You entered an argument with an inappropriate dimension.
You entered a matrix or vector dimension < 1 or > 255 or a noninteger.
You attempted to invert a matrix that is not a square matrix.
14 UNDEFINED
You are referencing a variable that currently is not defined.
15 MEMORY
Memory is insufficient to perform the desired command; you must delete
items from memory (Chapter 17) before executing this command.
16 RESERVED
You attempted to use a built-in variable inappropriately.
17 INVALID
You attempted to reference a variable or use a function where it is not valid.
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18 ILLEGAL NEST
You attempted to use an invalid function in an argument for
seq(
or a
CALC
function; for example,
der1(der1(x^3,x),x))
.
19 BOUND
You defined an upper bound that is less than the specified lower bound or a
lower bound that is greater than the specified upper bound.
20 GRAPH
WINDOW
One or more window variable values is incompatible with the others for
defining the graph screen; for example, you defined
xMax
<
xMin
.
Window variables are too small or too large to graph correctly; for
example, you attempted to zoom out beyond the calculator’s range.
21 ZOOM
A
ZOOM
operation resulted in an error; you attempted to define
ZBOX
with a line.
22 LABEL
In programming, the
Goto
instruction label is not defined with a
Lbl
instruction.
23 STAT
You attempted a stat calculation with at least one inappropriate list, such
as a list with less than two data points.
At least one element of a frequency list is < 0.
(
xMax
N
xMin
)
à
xScl
63 must be true when plotting a histogram.
24 CONVERSION
When converting measurements, the units are incompatible, as in volts to liters.
25 SOLVER
In the solver editor, the equation does not contain a variable.
You attempted to graph with the cursor positioned on bound.
26 SINGULARITY
In the solver editor, the equation contains a singularity, which is a point at
which the function is not defined.
27 NO SIGN CHNG
The solver did not detect a sign change.
28 ITERATIONS
The solver has exceeded the maximum permitted number of iterations.
29 BAD GUESS
The initial guess was outside the specified bounds.
The initial guess and several points around the guess are undefined.
Errors 26 through 29 occur
during the solving process.
Examine a graph of the
function or a graph of the
variable vs.
left
N
rt
in the
SOLVER
. If the equation has
a solution, change bounds
and
à
or the initial guess.
396
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30 DIF EQ SETUP
In
DifEq
graphing mode, equations in the equation editor must be from
Q'1
to
Q'9
and each must have an associated initial condition from
Q
[
1
to
Q
[
9.
31 DIF EQ MATH
The step size used by the fitting algorithm has become too small; check the
equations and initial values; try a larger value for the window variable
difTol
;
try changing
tMin
or
tMax
to examine a different region of the solution.
32 POLY
All coefficients are
0
.
33 TOL NOT MET
The algorithm cannot return a result accurate to the requested tolerance.
34 STAT PLOT
You attempted to display a stat plot that references an undefined list.
35 AXES
You attempted to plot a
DifEq
graph with improper axes set.
36 FLD
à
ORDER
You attempted to plot a 2nd-order or higher differential equation with
SlpFld
field format set; change field format or modify the order.
You attempted to plot a 3rd-order or higher differential equation with
DirFld
field format set; change field format or modify the order.
37 LINK MEMORY
FULL
You attempted to transmit an item with insufficient available memory in the
receiving unit; skip the item or cancel the transmission.
38 LINK
TRANSMISSION
ERROR
Unable to transmit item; check to see that the cable is firmly connected to
both units and the receiving unit is ready to receive data (Chapter 18).
You pressed ^ to break during transmission.
39 LINK
DUPLICATE NAME
You attempted to transmit an item when an item with the same name already
exists in the receiving unit.
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Equation Operating System (EOS™)
The Equation Operating System (EOS) governs the order of evaluation on the TI
-
86.
Calculations within parentheses are evaluated first, and then EOS evaluates functions
within an expression in this order:
1st Functions that are entered after the argument, such as
2
,
M
1
,
!
,
¡
,
r
, and conversions
2nd Powers and roots, such as
2^5
or
5
x
32
3rd Single-argument functions that precede the argument, such as
(
,
sin(
, or
log(
4th Permutations (
nPr
) and combinations (
nCr
)
5th Multiplication, implied multiplication, and division
6th Addition and subtraction
7th Relational functions, such as
>
or
8th Logic operator
and
9th Logic operators
or
and
xor
Implied Multiplication
The TI
-
86 recognizes implied multiplication, so you need not press
M
to express
multiplication in all cases. For example, the TI
-
86 interprets
2
p
,
4sin(46)
,
5(1+2)
, and
(2
¹
5)7
as
implied multiplication.
Parentheses
All calculations inside a pair of parentheses are completed
first. For example, in the expression
4(1+2)
, EOS evaluates
1+2
inside the parentheses first, and then multiplies
3
by
4
.
Within a priority level, EOS
evaluates functions from left
to right.
Multi-argument functions,
such as
nDeriv(A2,A,6)
, are
evaluated as they are
encountered.
TI
-
86 implied multiplication
rules differ from those of the
TI-85. For example, the TI
-
86
evaluates
1
à
2x
as
(1
à
2)
¹
x
,
while the TI-85 evaluates
1
à
2x
as
1
à
(2
¹
x)
.
398
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You can omit the close parenthesis (
)
) at the end of an expression. All open parenthetical
elements are closed automatically at the end of an expression. This is also true for open
parenthetical elements that precede the store or display-conversion instructions.
Open parentheses after list names, matrix names, or equation function names are not
interpreted as implied multiplication. Arguments that follow these open parentheses are
specified list elements, matrix elements, or values for which to solve the equation function.
TOL (The Tolerance Editor)
-
)
On the TI
-
86, the computational accuracy of some
functions is controlled by the variables
tol
and
d
. The
values stored to these variables may affect the speed at
which the TI
-
86 calculates or plots.
The variable
tol
defines the tolerance in calculating the functions
fnInt(
,
fMin(
,
fMax(
, and
arc(
,
and the
GRAPH
MATH
operations
G
f(x)
,
FMIN
,
FMAX
, and
ARC
(Chapter 6).
tol
must be a
positive value
1
E
L
12.
The value stored to
d
must be a positive real number.
d
defines the step size the TI
-
86 uses
to calculate the functions
arc
in
dxNDer
mode;
nDer
; and the operations
dy
à
dx
,
dr
à
d
q
,
dy
à
dt
,
dx
à
dt
,
INFLC
,
TANLN
, and
ARC
, all in
dxNDer
mode (Chapter 6).
To store a value to
tol
or
d
on the home screen or in a program, use
X
. You can select
tol
and
d
from the
CATALOG
. Also, you can enter
tol
directly and select
d
from the
CHAR
GREEK
menu.
Appendix
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Computational Accuracy
To maximize accuracy, the TI
-
86 carries more digits internally than it displays. Values are
stored in memory using up to 14 digits with a 3-digit exponent.
You can store values up to 12 digits long to most window variables. To
xScl
,
yScl
,
tStep
,
and
q
Step
, you can store values up to 14 digits long.
When a value is displayed, the displayed value is rounded as specified by the mode
setting (Chapter 1), with a maximum of 12 digits and a 3-digit exponent.
Chapter 4 describes calculations in hexadecimal, octal, and binary number bases.
400
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Support and Service Information
Product Support
Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands
For general questions, contact Texas Instruments Customer Support:
phone:
1
.
800
.
TI
.
CARES (1
.
800
.
842
.
2737)
e-mail:
ti-cares@ti.com
For technical questions, call the Programming Assistance Group of Customer
Support:
phone:
1.972.917.8324
Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands
Contact TI by e-mail or visit the TI
Calculator
home page on the World Wide Web.
e-mail:
ti-cares@ti.com
Internet:
education.ti.com
Appendix
401
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Product Service
Customers in the U.S. and Canada Only
Always contact Texas Instruments Customer Support before returning a product
for service.
Customers outside the U.S. and Canada
Refer to the leaflet enclosed with this product or contact your local Texas
Instruments retailer/distributor.
Other TI Products and Services
Visit the TI
Calculator
home page on the World Wide Web.
education.ti.com
402
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Warranty Information
Customers in the U.S. and Canada Only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product.
Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a
period of one (1) year from the original purchase date.
Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and
construction. THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR
UNREASONABLE USE, NEGLECT, IMPROPER SERVICE, OR OTHER CAUSES NOT ARISING OUT OF
DEFECTS IN MATERIALS OR CONSTRUCTION.
WARRANTY DISCLAIMERS. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE, INCLUDING
BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE, ARE LIMITED IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS
INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER
INCIDENTAL OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE
CONSUMER OR ANY OTHER USER.
Some states/provinces do not allow the exclusion or limitation of implied warranties or consequential damages, so
the above limitations or exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from
state to state or province to province.
Warranty Performance. During the above one (1) year warranty period, your defective product will be either
repaired or replaced with a reconditioned model of an equivalent quality, (at TI’s option) when the product is
returned, postage prepaid, to Texas Instruments Service Facility. The warranty for the repaired or replacement
unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than the
postage requirement, no charge will be made for such repair and/or replacement. TI strongly recommends that you
insure the product for value prior to mailing.
Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from
errors or meet your specific requirements. All software is provided “AS IS.”
Copyright. The software and any documentation supplied with this product are protected by copyright.
Appendix
403
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Australia & New Zealand Customers only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments electronic product warranty extends only to the original purchaser and user
of the product.
Warranty Duration. This Texas Instruments electronic product is warranted to the original
purchaser for a period of one (1) year from the original purchase date.
Warranty Coverage. This Texas Instruments electronic product is warranted against defective
materials and construction. This warranty is void if the product has been damaged by accident or
unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or
construction.
Warranty Disclaimers. Any implied warranties arising out of this sale, including but not
limited to the implied warranties of merchantability and fitness for a particular purpose,
are limited in duration to the above one-year period. Texas Instruments shall not be liable
for loss of use of the product or other incidental or consequential costs, expenses, or
damages incurred by the consumer or any other user.
Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential
damages, so the above limitations or exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that
vary from jurisdiction to jurisdiction.
Warranty Performance. During the above one (1) year warranty period, your defective product will
be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TI’s
option) when the product is returned to the original point of purchase. The repaired or replacement
unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other
than your cost to return the product, no charge will be made for such repair and/or replacement. TI
strongly recommends that you insure the product for value if you mail it.
Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be
free from errors or meet your specific requirements. All software is provided “AS IS.”
Copyright. The software and any documentation supplied with this product are protected by
copyright.
404
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All Customers outside the U.S. and Canada
For information about the length and terms of the warranty, refer to your package and/or to the warranty
statement enclosed with this product, or contact your local Texas Instruments retailer/distributor.
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 405 of 15
Index
" (string),
216, 227
" (List Editor menu),
156
! (factorial),
294
,
362
(greater than or equal to),
56
,
301
(less than or equal to),
55
,
312
ƒ
(not equal to),
56
,
326
p (pi),
48
(square root),
360
ˆ
(square root) key,
48
v
(statistical result variable),
193
w
(statistical result variable),
193
L
1
(inverse),
48
,
309
dim,
184
,
281
dimL,
282
f(x) (function numerical
integral),
96
,
98
@
Tbl (table step),
113
s
x (statistical result variable),
193
G
x
2
(statistical result variable),
193
s
y (statistical result variable),
193
% (percent),
52
,
334
< (less than),
55
,
312
= (assign to),
270
= (equals),
290
== (relational equals),
55
,
291
> (greater than),
55
,
300
[ ],
319
,
369
^ (exponent),
48
{ },
316
10^ (10 raised to
n
power),
48,
337
A
abs (absolute value),
49
,
71
,
175
,
185
,
267
addition (+),
267
ALL,
43
,
232
ALL
N
,
77
ALL+,
77
ALPHA character,
22
ALPHA cursor,
22
alpha cursor,
22
ALPHA key,
21
ALPHA-lock,
22
,
44
canceling,
22
setting,
22
and (Boolean),
69
,
268
angle,
71
,
175
,
185
,
269
expressed in degrees,
51
angle modes,
35
angle values,
35
Ans (last answer),
29
,
30
,
41
,
269
answer
displaying,
19
storing to a variable,
41
APD.
See
Automatic Power Down
ARC,
96
,
98
arc(,
54, 269
argument,
25
Asm (assembly language
program),
269
AsmComp (compile assembly
language program),
226
,
270
AsmPrgm (assembly language
program),
226
,
270
assembly language programs,
225
assignment,
270
attached formulas
executing,
164
resolving errors,
165
attached-formula list
comparing,
163
creating,
162
editing elements,
166
aug(,
160, 184
,
270
Automatic Power Down,
17
automatic regression equation
storage,
191
AXES,
137
Axes editor,
137
field formats,
137
Axes(,
271
AxesOff,
84
,
271
AxesOn,
84
,
271
B
Ü
(binary),
271
backup battery,
16
406
Index
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 406 of 15
BASE
Õ
-
Ú
(Hexadecimal) menu,
67
BASE BIT menu,
69
BASE BOOL (Boolean) menu,
68
BASE CONV (Conversion)
menu,
68
BASE menu,
66
BASE TYPE menu,
67
base type symbol,
67
batteries,
2
,
16
-
18
battery compartment,
16
BCKUP (memory backup),
237
Bin (binary),
35
,
272
4
Bin (to binary),
68
,
272
binary integer,
271
binary number base,
35
,
66
Boolean operators,
68
,
268
,
325
,
328
,
370
bound={
L
1E99,1E99},
204
bounds,
204
BOX (GRAPH ZOOM menu),
14, 92
,
93
Box (stat plot),
272
BOX (ZOOM menu),
208
break (program),
222
BREAK menu,
26
built-in constants,
58
built-in variables,
39
,
45, 138
busy indicator,
26
,
85
C
CALC (Calculus) menu,
54
calculating derivatives,
7
calculation
interrupting,
26
calculus functions,
54
CATALOG,
25
,
38
Quick-Find Locator,
262
CATLG (CATALOG),
43
CATLG-VARS (CATALOG
Variables) menu,
43
changing
TI
-
86
settings,
39
CHAR (Character) menu,
45
CHAR GREEK menu,
46
CHAR INTL (International)
menu,
46
CHAR MISC (Miscellaneous)
menu,
46
characters,
19
alpha,
22
blue,
21
,
22
case,
22
characters (continued)
deleting,
23
entering, 21
second,
22
yellow,
21
check RAM screen,
230
CIRCL (circle),
105
,
106
Circl(,
273
circles
drawing,
106
CLDRW (clear drawing),
103
,
105
,
273
clearing CUSTOM menu items,
45
clearing ENTRY storage area,
29
ClLCD (clear LCD),
216
,
273
ClrEnt (clear entry),
232
,
273
ClTbl (clear table),
114
,
216
,
273
cnorm (column norm),
183, 273
command line,
220
complements (binary numbers),
66
complex matrix,
180
Complex Number menu,
71
complex number modes,
35
complex number variables,
43
complex numbers,
29
,
70
as list elements,
156
displaying as result,
5
entering,
20
in results,
70
separator,
70
using in expressions,
71
complex values,
48
concatenation (+),
274
cond (condition number),
183
,
274
conj (complex conjugate),
71
,
175
,
185
,
275
connecting instructions,
235
CONS (constants),
43
CONS (Constants) menu,
58
CONS BLTIN (Built-In
Constants) menu,
58
CONS EDIT menu,
60
consecutive entries,
26
Constant Memory feature,
17
,
34
constants,
59
built-in,
58
defined,
58
name,
61
user-created,
58
,
60
Index
407
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 407 of 15
contrast
adjusting,
2
,
18
CONV (Conversions) menu,
62
CONV AREA menu,
63
CONV ENRGY (Energy) menu,
64
CONV FORCE menu,
64
CONV LNGTH (Length) menu,
63
CONV MASS menu,
64
CONV POWER menu,
64
CONV PRESS (Pressure) menu,
64
CONV SPEED menu,
64
CONV TEMP (Temperature)
menu,
8
,
63
CONV TIME menu,
63
CONV VOL (Volume) menu,
63
conversions
4
Bin,
272
4
Dec,
279
4
DMS,
51
,
285
4
Frac,
52
,
298
4
Hex,
303
4
Oct,
327
4
Pol,
336
4
REAL,
156
conversions (continued)
4
Rec,
343
4
Sph,
360
Eq
4
St,
227
li
4
vc,
160
St
4
Eq(,
227, 361
vc
4
li,
160
converting a value expressed as
a rate,
65
converting Fahrenheit to
Celsius,
8
converting units of measure,
61
CoordOff,
84
,
275
CoordOn,
84
,
275
copying variable value,
41
corr (correlation coefficient),
193
cos (cosine),
48
,
186
,
276
cos
L
1
(arccosine),
48
,
276
cosh (hyperbolic cosine),
51
,
277
cosh
L
1
(inverse hyperbolic
cosine),
51
,
277
CPLX (complex number
variables),
43, 71
cross(,
173
,
277
cSum( (cumulative sum),
160,
278
current entry,
19
clearing,
23
current item,
38
cursor,
17
,
22
ALPHA,
22
alpha,
22
changing,
23
direction keys,
23
entry,
22
free-moving,
128
,
144
,
205
full,
22
insert,
22
location,
19
,
20
,
21
,
25
moving,
23
second,
22
selection,
38
trace,
90
curves
drawing,
107
CUSTOM menu,
44
clearing items,
45
copying items,
44
Customer Support,
392
4
Cyl (to cylindrical),
174
,
278
CylV (cylindrical vector
coordinate mode),
36
,
278
D
Þ
(decimal),
278
data type selection screen,
42
Dec (decimal number base
mode),
278
Dec (decimal),
35
,
65
4
Dec (to decimal),
279
decimal,
20
decimal mode,
34
,
35
,
65
fixed (012345678901),
35
floating,
35
decimal number,
278
decimal number base,
35
decimal point,
35
degree angle mode,
35, 75
,
279
degree complex-number mode,
70
degree entry (
¡
),
279
degrees
¡
,
51
degrees/minutes/seconds form,
51
DELc (delete column),
179
DELET,
60
408
Index
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 408 of 15
DELf (delete function),
77
DELi (delete element),
170
DELr (delete row),
179
Deltalst( (delta list),
160
,
279
DelVar( (delete variable),
219,
280
der1( (first derivative),
54, 280
der2( (second derivative),
54,
280
derivatives
calculating,
7
det (determinant),
183
,
281
DFLTS (defaults),
232
DifEq (differential equation
mode),
35
,
74
,
239
,
281
differential equation editor,
134
differential equation graphs,
74
displaying,
138
drawing,
145
mode,
35
differential equations
changing to first order,
142
defining graph,
132
drawing solutions,
148
DrEqu(,
287
editor,
134
EXPLR,
148
differential equations (continued)
graphing,
132
,
137
,
139
,
141
,
142
initial conditions editor,
136
mode,
144
Q'n equation variables,
135
setting axes,
137
setting graph format,
133
setting graphing mode,
132
solving,
139
tracing,
144
using EVAL,
150
window variables,
135
differentiation modes,
36
difTol (tolerance),
136
dim (dimension),
173
,
184
,
281
dimL (dimension of list),
159,
282
DirFld (direction field),
134
,
282
Disp (display),
216
,
283
DispG (display graph),
283
display,
17
display contrast
adjusting,
17
,
18
displaying a menu,
31
DispT (display table),
284
DIST (distance),
96
,
98
division (/),
284
division symbol,
3
4
DMS (to degrees/
minutes/seconds),
51
,
285
dot(,
173
,
285
dr/d
q
,
122
DRAW,
75
,
88
DrawDot,
84
,
285
DrawF (draw function),
103
,
107
,
286
drawing
circles,
106
differential equation graphs,
145
freehand points, lines,
curves,
107
function, tangent line,
inverse function,
107
line segments,
105
lines,
105
,
106
parametric graphs,
130
points,
108
polar graphs,
122
drawing tools,
101
drawings
clearing,
103
drawings (continued)
recalling,
102
saving,
102
DrawLine,
84
,
286
DrEqu( (draw equation),
145,
287
DrInv (draw inverse),
103
,
107
,
287
DS<( (decrement and skip),
219, 288
DUPLICATE NAME menu,
241
dx/dt,
130
dxDer1 (exact differentiation),
36
,
75, 288
dxNDer (numeric
differentiation),
36
,
75,
288
dy/dt,
130
dy/dx,
96
,
99
,
130
E
E
(exponent),
48, 292
e^ (e raised to power),
288
editing equations,
205
editor menu,
33
eigVc (eigenvector),
183
,
289
eigVl (eigenvalue),
183
,
289
Index
409
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 409 of 15
element
matrix,
181
ellipsis
at end of line,
19
in matrix row,
179
Else,
218
,
306
e-mail address (TI Customer
Support),
392
End,
218
,
290
,
297
,
306
Eng (engineering notation),
34,
20
,
290
entry
executing,
19
storing to,
29
entry cursor,
18
,
22
,
23
[ENTRY] key,
19
ENTRY Storage Area,
28
,
29
EOS.
See
Equation Operating
System
Eq
4
St( (equation to string),
227,
290
eqn (equation) variable,
54
,
203, 205
EQU (equation variables),
43
equal (=),
290
equal to (==),
291
equation
entering,
203
evaluating,
122
,
130
equation coefficients
storing to a variable,
210
equation editor,
74
,
75
,
76
,
80
entering a function,
77
graph styles,
77
parametric,
126
polar,
118
Equation Editor menu,
76
Equation Operating System,
397
equation results
storing to a variable,
210
equation solver,
40
,
202
graph tools,
207
equation storage
automatic regression,
191
equation variables,
40
,
43
,
78
equation-entry editor,
203
equations
editing,
205
solving,
206
error conditions,
393
error menu,
31
error message,
27
error type,
27
errors,
17
,
27
correcting,
27
diagnosing,
27
from attached formulas,
165
EStep,
136
Euler method,
133
,
291
eval,
52
,
76
,
88
,
101
,
122
,
130
,
150
,
291
evalF(,
54
,
292
evaluating a function for x,
101
evaluating equations,
122
,
130
e
x
(constant e raised to a
power),
48
exact differentiation,
36
EXIT (cancel data
transmission),
241
exiting a menu,
6
,
33
exp variable,
54,
203
EXPLR (explore),
148
exponent (
å
),
292
ExpR (exponential regression),
190, 293
expression,
18
,
20
,
24
,
25
,
26
,
30
,
48
editing,
4
entering,
24
expression (continued)
entering a list,
153
evaluating,
29
,
30
using a complex number,
71
using a vector,
172
using matrix,
181
F
factorial (!),
50
,
294
Fahrenheit
converting to Celsius,
8
family of curves
graphing,
86
in parametric graphs,
129
in polar graphs,
120
fcstx (forecast x),
294
fcsty (forecast y),
294
feature symbol,
39
field formats,
134
Fill,
184
Fill(,
160
,
173
,
295
Fix,
295
FldOff (slope and direction
fields off),
134, 295
fldPic (field) variable,
138
Float,
35
,
295
410
Index
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 410 of 15
FMAX (function maximum),
96
,
97
fMax( (function maximum),
54,
296
FMIN (function minimum),
96
,
97
fMin( (function minimum),
54,
296
fnInt( (function integral),
54,
296
FnOff (functions off),
296
FnOn (functions on),
297
For(,
218
,
297
Form(,
161
,
298
FORMT (graph format),
76
formulas
attaching,
163
attaching to list name,
162
detaching,
166
fPart (fractional part),
49
,
176
,
186
,
298
4
Frac (to fractions),
52
,
298
fraction,
3
,
19
free-moving cursor,
84
,
144
parametric graphs,
128
polar graphs,
119
fStat (frequency list),
189
full cursor,
22
Func (function mode),
35
,
74
,
239
,
299
function graphs,
73
,
74
mode,
35
functions,
25
,
38
deleting,
77
deselecting,
13
drawing,
107
entering,
25
entering in the equation
editor,
76, 77
,
78
evaluating,
101
keyboard,
48
plotting,
11
tracing,
11
using with lists,
5, 161
G
gcd( (greatest common
denominator),
52, 299
GDB (graph database),
43
GDB variable,
102
Get(,
299
getKy (get key),
216
,
300
key code diagram,
217
GOTO,
26
,
27
,
300
Goto (PRGM CTL menu),
219
,
224
graph,
75
defining,
74
displaying,
85
family of curves,
86
interrupting,
26
modifying,
85
pausing,
85
shading,
104
stopping,
85
GRAPH (Solver menu),
206
graph database (GDB),
102
recalling,
76
GRAPH DRAW menu,
75
,
103
,
122
,
145
graph format
differential equations,
133
,
137
parametric graphs,
128
polar graphs,
119
screen,
76
setting,
83
GRAPH LINK,
235
GRAPH MATH menu,
75
,
95
,
122
,
130
GRAPH MATH operations
effect of other settings,
96
using
f(x), DIST, or ARC,
98
using dy/dx or TANLN,
99
using ISECT,
100
using ROOT, FMIN, FMAX,
or INFLC,
97
using YICPT,
100
GRAPH menu,
27
,
31
,
75
,
88
,
117
,
126
,
133
graph modes,
35
setting,
74
differential equations, 144
function,
parametric,
126
polar,
35, 117
graph screen,
75
setting window variables,
81
graph screen dimensions,
75
graph styles,
79
changing,
10
GrStl(,
302
setting,
79
graph tools
in differential equation
graphs,
144
in equation solver,
207
Index
411
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 411 of 15
graph tools (continued)
in parametric graphs,
128
in polar graphs,
119
graph zoom
defining custom,
93
defining screen,
92
setting zoom factors,
93
Smart Graph, 94
zooming in,
92
,
93
zooming out,
92
,
93
GRAPH ZOOM menu,
75
,
91
,
147
graphing accuracy,
89
greater than (>),
300
greater than or equal to (
),
301
grid points,
84
GridOff,
84
,
301
GridOn,
84
,
302
GrStl( (graph style),
220, 302
Guess,
204
in interactive solver editor,
205
H
ß
(hexadecimal),
302
Hex (hexadecimal),
35, 302
4
Hex (to hexadecimal),
68
,
303
hexadecimal characters menu,
67
hexadecimal number base,
35
,
66
Hist (histogram),
303
home screen,
17
,
18
,
23
,
24
,
26
,
27
displaying entries and
answers,
18
Horiz,
304
HORIZ (horizontal line),
105
,
106
hyperbolic functions,
51
I
IAsk,
304
IAuto,
304
ident (identity),
184, 304
If,
218
,
305
,
306
imag (imaginary),
71, 175
,
185,
306
imaginary portion of complex
number,
71
implied multiplication,
397
INFLC (inflection point),
96
,
97
INITC (initial conditions),
136
InpSt,
217, 307
Input (PRGM I/O menu),
216,
307
Input CBLGET,
216
INSc (insert column),
179
insert cursor,
22
,
23
canceling,
23
INSf (insert function),
77
INSi (insert element),
170
INSr (insert row),
179
installing batteries,
16
instructions,
25
entering,
25
executing,
19
int (integer),
49
,
176
,
186, 308
integer part,
49
integer part of real numbers
displaying,
6
inter( (interpolate),
309
interactive-solver editor,
204
bounds,
204
international letters,
46
Internet
downloading programs,
235
e-mail address (TI Customer
Support),
392
interpolate/extrapolate editor,
53
interrupting a calculation,
26
interrupting a graph,
26
,
27
interrupting a program,
222
inverse,
309
inverse function
drawing,
107
IPart (integer part),
6, 49
,
176
,
186, 309
IS>( (increment and skip),
219,
310
ISECT (intersection),
96, 100
items on menus,
31
K
keys,
48
2nd,
21
ALPHA,
21
primary function,
19
,
21
,
22
key code diagram,
217
L
LabelOff,
84
,
310
LabelOn,
84
,
310
412
Index
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 412 of 15
last answer,
28
,
29
storing to variable,
3
last entry,
26
,
28
Lbl (label),
219
,
224, 311
lcm( (least common multiple),
52, 311
LCust( (load custom menu),
220, 311
left
N
rt,
202
length of segment of curve,
54
less than (<),
312
less than or equal to (
),
312
LgstR (logistic regression),
190,
193, 313
li
4
vc (list to vector),
160
,
174
,
316
LINE,
104
,
105
Line(,
314
Lines
drawing,
107
LINK menu,
236
LINK SEND menu,
236
LINK SEND85 menu,
239
linking instructions,
235
linking options,
234
LinR (linear regression),
190
,
315
list,
29
,
43
,
52
as an argument,
161
attached formulas,
165
attaching formula,
162
,
166
braces { },
316
comparing,
163
creating,
157
deleting an element,
158
deleting from memory,
154
detaching formulas,
166
displaying list elements,
154
editing elements,
166
entering in an expression,
153
inserting,
157
removing from list editor,
158
storing,
154
uses,
152
using with function,
5
list editor,
31
,
67
,
156
,
188
attaching formulas,
163, 164
removing a list,
158
List Editor menu, 156
list element
complex,
156
deleting,
158
list element (continued)
displaying,
155
,
158
editing,
158
storing a value to,
155
list entry { },
316
LIST menu,
152
list names,
43
LIST NAMES menu,
153
,
189
LIST OPS menu,
159
ln (natural log),
48
,
316
lngth (length of string),
227
,
316
LnR (logarithmic regression),
190
,
317
log,
48
,
318
low-battery message,
16
,
18
lower menu,
32
LU( (lower-upper),
183
,
318
M
Macintosh
linking to,
235
MATH,
75
MATH (Graph menu),
88
MATH ANGLE menu,
51
MATH HYP (Hyperbolic) menu,
51
MATH menu,
31
,
49
MATH MISC (Miscellaneous)
menu,
52
MATH NUM (Number) menu,
31, 49
MATH PROB (Probability)
menu,
50
mathematical functions,
48
using with lists,
161
with a matrix,
185
matrix,
29
brackets [ ],
180
,
319
creating,
178
,
180
defined,
178
deleting from memory,
180
displaying elements, rows,
submatrices,
181
editing using
X
,
182
names,
43
using in expression,
181
using math functions,
185
Matrix Editor menu,
179
matrix entry [ ],
319
MATRX (matrix names),
43
MATRX (Matrix) menu,
178
MATRX CPLX (Complex)
menu,
185
Index
413
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 413 of 15
MATRX MATH menu,
183
MATRX NAMES menu,
178
MATRX OPS (Operations)
menu,
184
max(,
49
,
160
,
319
maximum characters,
22
maxX,
193
maxY,
193
MBox,
319
Med (median),
193
MEM (clear memory),
232
MEM (Memory) menu,
29
,
230
MEM RESET menu,
232
MEM DELET (Delete) menu,
231
MEM FREE (available
memory),
230
memory,
16
,
17
,
22
,
28
,
29
,
223
available,
230
deleting items,
231
resetting,
3
,
232
memory backup
initiating,
237
overwrite warning,
237
menus
displaying,
31
exiting,
6
menus (continued)
in editors,
33
keys,
32
lower,
32
removing,
6
,
33
selecting items,
32
upper,
33
menu map,
380
Menu(,
219
,
320
min(,
49
,
160
,
320
minX,
193
minY,
193
mod(,
49
,
320
mode settings,
19
,
20, 70
changing,
34
displaying,
34
number base,
65
modulo,
49
mRAdd,
184
mRAdd(,
321
multiple entries
retrieving,
29
multiplication (
¹
),
321
multR( (multiply row),
184,
322
N
n (statistical results variable),
193
natural log,
48
nCr (number of combinations),
50, 322
nDer( (numerical derivative),
54, 323
negation symbol (
L
),
20
negative numbers
entering,
19
norm,
173
,
183
,
323
Normal,
34
,
324
not (Boolean),
66
,
69
,
325
not equal to (
ƒ
),
326
notation modes,
34
engineering,
34
normal,
34
scientific,
34
notation of displayed answers,
20
nPr (number of permutations),
50, 326
number base,
65
designators,
65
ranges,
66
type, designating,
67
modes,
35
numbers
entering, 19
numeric differentiation,
36
numerical derivative,
54
O
Ý
,
326
Oct (octal),
35, 327
4
Oct (to octal),
327
octal integer,
326
octal number base,
35
,
66
OneVa (OneVar),
189, 191
,
327
operation
second,
22
operator
entering,
25
or (Boolean),
69
,
328
order of operations,
56
order-of-evaluation rules,
20, 62
Outpt(,
217, 329
OVERW (overwrite),
241
414
Index
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 414 of 15
P
P2Reg (quadratic regression),
190, 330
P3Reg (cubic regression),
190,
331
P4Reg (quartic regression),
190, 332
panning,
90
Par,
74
Param (parametric mode),
35
,
239, 333
parametric equation
deleting,
127
graphing,
126
selecting and deselecting,
127
parametric graphs,
74
default graph style,
126
defining,
125
displaying,
128
drawing,
130
equation editor,
126
free-moving cursor,
128
graph format,
128
graph tools,
128
mode,
35
,
126
tracing,
128
window variables,
127
Zoom,
129
parentheses,
20
,
25
,
56
,
61
,
397
pause,
26
,
333
Pause (PRGM CTL menu),
219
pause indicator,
26
PC
linking to,
235
PEN,
105
percent (%),
334
permutations of items,
50
pEval(,
52, 334
phone (TI Customer Support),
392
pi,
59
PIC (picture names),
43
PIC variable
entering,
76
storing graph,
102
pictures
recalling,
102
saving,
102
pixel resolution
for function graphs,
81
PlOff (plot off),
195, 334
PlOn (plot on),
195, 334
PLOT1,
195
Plot1(,
335
PLOT2,
195
Plot2(,
335
PLOT3,
195
Plot3(,
335
plotting functions,
9
,
11
plotting statistical data,
194
points
drawing,
108
turning on and off,
108
Pol (polar mode),
35
,
74, 239
,
336
4
Pol (to polar),
71, 174, 336
polar angle of complex number,
72
polar complex (
),
336
polar complex mode,
35, 336
polar complex number form,
20, 70
polar equation
tracing,
120
polar graphs,
74
,
84
default graph style,
118
defining,
117
displaying,
119
drawing,
122
equation editor,
118
free-moving cursor,
119
graph format,
119
graph tools,
119
polar graphs (continued)
mode,
35
trace cursor,
120
,
121
tracing,
120
window editor,
118
Zoom,
121
PolarC (polar complex mode),
35, 336
PolarGC (polar graph
coordinates),
84, 336
poly,
337
polynomial coefficient
storing to a variable,
212
polynomial root
storing to a variable,
212
polynomial root-finder,
211
polynomial value,
52
power of 10 (10^),
20
,
34, 337
PRegC,
193
previous entries,
8
re-executing,
19
retrieving,
28
Index
415
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 415 of 15
reusing,
28
PRGM (program names),
43
PRGM CTL menu,
218
PRGM I/O (Input/Output) menu,
215
PRGM menu,
214
prod (product),
52
,
160, 338
program editor,
214
menus and screens,
215, 220
program flow,
56
programming
assembly language,
225
calling a program,
224
copying a program,
225
creating programs,
214
defined,
214
deleting a program,
223
downloading assembly
programs,
225
editing a program,
223
entering a command line,
220
getting started,
214
interrupting program,
222
running program,
221
using variables,
225
Prompt (PRGM I/O menu),
216
,
338
prompts,
22
Eval x=,
76
Name=,
22
,
39
,
76
Rcl,
42
Sto,
212
PTCHG,
105
PtChg(,
338
PTOFF,
105
,
108
PtOff(,
338
PTON,
105
,
108
PtOn(,
338
PwrR (power regression),
190
,
339
PxChg(,
103
,
340
PxOff(,
103
,
340
PxOn(,
103
,
340
PxTest(,
103
,
340
Q
Q'n equation variables,
135
Qrtl1,
193
Qrtl3,
193
Quick Zoom,
91
in parametric graphing,
129
in polar graphing,
120
Quick-Find Locator (A to Z
Reference),
262
R
r
(radian entry),
341
rAdd,
184
rAdd(,
340
Radian (angle mode),
35
radian angle mode,
75
,
341
radian complex-number mode,
70
radian entry (
r
),
341
rand (random),
50
,
341
randBin( (random binomial),
50, 341
randInt( (random integer),
50,
342
randM( (random matrix),
184,
342
randNorm( (random normal),
50, 342
random number,
50
RCGDB (recall graph
database),
76
,
88
,
343
RcPic (recall picture),
76
,
102,
343
RCPIC menu,
76
REAL,
43
,
175
,
185
,
343
4
REAL (to real number),
156
,
170
,
179
real number variables,
43
real numbers,
29
real portion of complex
number,
71
4
Rec (to rectangular),
71
,
174
,
343
recalling variable values,
18, 42
receiving transmitted data,
241
rectangular complex mode,
35
rectangular complex numbers,
70
rectangular complex-number
form,
20
rectangular graph,
84
rectangular vector coordinates,
36
RectC (rectangular complex),
35
,
344
RectGC (rectangular graph
coordinates),
84, 344
RectV (rectangular vector
coordinate mode),
36, 344
RECV (LINK menu),
236
416
Index
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 416 of 15
RECV (LINK SND85 menu),
240
redefining user-created
constants,
60
ref (row echelon form),
184
,
344
regression models,
191
relational functions,
55
,
56
RENAM (rename),
241
Repeat (PRGM CTL menu),
218, 345
replacing batteries,
16
resetting memory,
232
result,
20
,
24
result of last expression,
26
Return (PRGM CTL menu),
219,
345
RK (Runge-Kutta) method,
133
,
345
rnorm (row norm),
183
,
346
ROOT, 96,
97
x
,
346
root-finder,
211
RotL (rotate left),
69
,
347
RotR (rotate right),
69
,
347
round(,
49
,
176
,
348
row
of matrix,
181
rref (reduced row echelon),
184, 348
rSwap( (row swap),
184, 348
running a program,
221
S
Scatter (stat plot type),
349
Sci (scientific notation),
20, 34,
349
scrolling,
19
seed value,
50
SELCT,
112
SELECT,
77
Select(,
161
,
350
selection cursor,
38
SEND (LINK menu),
236
SEND WIND screen,
238
Send(,
216, 350
separator,
70
seq( (sequence),
52,
160, 351
SeqG (sequential graphing),
84,
351
series of instructions
displaying,
18
SetLE,
159
SetLEdit,
161
,
351
setting graph format,
83
setting graph style,
80
Shade(,
103
,
104
,
352
shading
pattern,
104
resolution,
104
shading patterns,
80
ShftL (shift left),
69
,
353
ShftR (shift right),
69
,
353
ShwSt (show string),
354
sign,
49
,
354
SimulG (simultaneous
graphing),
84
,
354
SIMULT ENTRY menu,
208
SIMULT order screen,
208
SIMULT RESULT menu,
209
simult(,
210
,
354
simultaneous equation solver,
208
sin (sine),
48
,
186
,
355
sin
L
1
(arcsine),
48
,
355
sine
calculating,
3
sinh (hyperbolic sine),
51
,
356
sinh
L
1
(inverse hyperbolic sine),
51
,
356
SinR (sinusoidal regression),
190
,
193, 357
SKIP,
241
SlpFld (slope field),
134
,
358
Smart Graph,
86
drawing tools,
102
in GRAPH MATH,
95
in Graph Zoom,
94
SND85 (LINK menu),
236
solution method formats,
133
solutions
drawing,
148
SOLVE,
205
solver graph,
207
Solver menu,
206
Solver ZOOM menu,
208
Solver(,
358
solving differential equations,
139
solving for unknown variable,
206
sortA,
159
,
359
sortD,
159
,
359
Sortx,
160, 359
Sorty,
160, 359
4
Sph (to spherical),
174
,
360
Index
417
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 417 of 15
SphereV (spherical vector
coordinate mode),
36
,
360
square (
2
),
360
square root (
),
7, 360
St
4
Eq( (string to equation),
227,
361
STAT (statistical result
variables),
43
STAT CALC (Calculations)
menu,
189
STAT menu,
188
Stat Plot
changing on/off status,
81
setting up,
195
turning on and off,
195
STAT PLOT menu,
195
STAT PLOT status screen,
194
STAT VARS (Statistical
Variables) menu,
192
statistical analysis,
188
results,
192
statistical data
entering,
189
plotting,
194
,
195
STGDB (store graph database),
76
,
88
,
361
STOa,
210
STOb,
210
Stop,
219, 362
Store,
18
store symbol,
22
store to variable (
),
362
storing a graph display, 102
storing data,
39
storing equation coefficients,
210
storing equation results,
210
STOx,
210
STPIC (store picture),
76, 88
,
362
STPIC menu,
76
StReg (store regression
equation),
190, 362
string,
29
concatenating,
226
creating,
226
defined,
226
storing,
226
,
227
string entry,
363
STRNG (string variables),
43
STRNG (String) menu,
227
STYLE,
77
sub( (subset of string),
227, 363
submatrix
displaying,
181
subroutines,
224
subtraction (
N
),
363
sum,
52
,
160
,
364
sum of elements of list,
52
Sx (statistical result variable),
193
syntax error,
27
syntax of function,
25
syntax of instruction,
25
T
T
(transpose),
367
table,
110
clearing,
114
displaying,
110
navigating,
111
setting up,
113
setup editor,
113
TABLE menu,
110
Table menus,
112
table setup editor,
113
tan (tangent),
48
,
364
tan
L
1
(arctangent),
48
,
365
tangent line
drawing,
107
tanh (hyperbolic tangent),
51
,
365
tanh
L
1
(inverse hyperbolic
tangent),
51
,
365
TANLN (tangent line),
96
,
99
TanLn(,
103
,
107, 366
TBLST (table setup editor),
112, 113
TEST menu, 55
TEXT,
105
Text(,
366
Then,
218
,
305
,
306
TI-GRAPH LINK,
235
tMax,
127
,
136
tMin,
127
,
136
TOL (Tolerance Editor),
398
tPlot,
136
TRACE,
88
TRACE (cursor),
75
Trace (Graph menu),
367
TRACE (Solver menu),
207
trace cursor,
75
,
90
,
144
,
205
in parametric graphing,
128
in polar graphing,
120
moving,
90
,
121
,
129
panning,
90
Quick Zoom,
91
418
Index
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 418 of 15
stopping and resuming,
91
tracing a function,
11
transmitting data,
234
,
240
error conditions,
242
insufficient memory,
242
transmitting data (continued)
repeating to several devices,
242
selecting variables,
238
window variables,
239
transpose (
T
),
367
tStep,
127
,
136
,
138
turning off TI-86,
2, 17
turning on TI-86,
2, 17
TwoVa (TwoVar),
189, 368
U
unevaluated expression
storing,
9
,
40
units of measure
converting,
61
unit-to-unit cable,
234, 235
unitV (unit vector),
173
,
368
unknown variable
solving for,
206
upper menu,
32
selecting an item,
33
user-created constants,
43
,
58
,
60
user-created zoom variables,
239
V
value,
24
,
25
,
29
variable,
21
classifying as data types,
42
copying,
41
creating,
39
deleting,
45
displaying,
41
in expressions,
4
in table screen,
111
names,
44
recalling,
42
storing data to,
39
storing results to,
3, 30
uppercase and lowercase
names,
39
x variable,
77
y variable,
77
variable equations
in a table,
114
VARS CPLX (complex
variables) screen,
71
VARS EQU menu,
203
vc
4
li (vector to list),
160
,
174,
369
vector,
29
brackets [ ],
369
complex,
171
,
180
creating,
170
defined,
168
deleting from memory,
170
displaying,
171
editing dimension and
elements,
172
forms,
168
operations,
173
using in an expression, 172
with math functions,
176
vector coordinate modes,
36
vector editor,
168
Vector Editor menu,
170
vector entry [ ],
369
VECTR (vector names),
43
VECTR CPLX (Complex) menu,
175
VECTR MATH menu,
173
VECTR menu,
169
VECTR NAMES menu,
169
VECTR OPS (Operations)
menu,
173
VERT (vertical line),
104
,
106
,
369
W
warranty information,
400
,
402
While,
218, 369
WIND (Solver menu),
206
WIND (window variables),
43,
35
,
75, 238
window editor,
75
polar,
118
window variables,
82
@
x and
@
y,
83
changing,
12
,
82
differential equations,
135
graph screen,
81
X
x variable,
77
XMIT (transmit),
237
,
240
Xor (Boolean),
69
,
370
xRes (resolution),
81
xScl (scale),
81
xStat (x-variable list),
189
Index
419
99INDEX.DOC TI-86, Index, US English Bob Fedorisko Revised: 02/13/01 2:51 PM Printed: 02/27/01 1:29 PM Page 419 of 15
xyline,
370
Y
y variable,
77
y(x)=,
75
YICPT (y-intercept),
96, 100
yScl (scale),
81
yStat (y-variable list),
189
Z
ZData,
371
ZDATA (GRAPH ZOOM menu),
92
ZDecm,
372
ZDECM (GRAPH ZOOM menu),
92
ZFACT (ZOOM FACTOR),
92,
208
ZFit,
129
,
373
ZFIT (GRAPH ZOOM menu),
92
ZIn (zoom in),
373
ZIN (zoom in),
92
,
208
ZInt,
374
ZINT (GRAPH ZOOM menu),
92
ZOOM,
14
,
75
,
88
custom,
93
parametric graphs,
129
polar graphs,
121
ZOOM operations,
147
zoom window variables
storing and recalling,
95
ZOOMX (GRAPH ZOOM menu),
92
ZOOMY (GRAPH ZOOM menu),
92
ZOUT (zoom out),
92
,
208
,
375
ZPREV (zoom previous),
92
,
375
ZRCL (GRAPH ZOOM menu),
92
,
95
user-created zoom variables,
239
ZRcl (zoom recall),
376
ZSqr,
376
ZSQR (GRAPH ZOOM menu),
92
ZSTD (GRAPH ZOOM menu),
92
ZSTD (standard defaults),
208
,
377
ZSTO (GRAPH ZOOM menu),
92
,
95
ZTrig,
378
ZTRIG (GRAPH ZOOM menu),
92
6

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