degrees to radians.

value {value1,value2,value3,value4,.,value n}
also designates degrees (D) in DMS format. ' (minutes) designates minutes (M) in DMS format. " (seconds) designates seconds (S) in DMS format.
Note: " is not on the ANGLE menu. To enter ", press [].

(Radians)

(radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use r to convert radians to degrees.

valuer

Degree mode
8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line.

answer8DMS

R8Pr (, R8Pq(, P8Rx(, P8Ry(
R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( converts rectangular coordinates to polar coordinates and returns q. x and y can be lists. R8Pr(x,y), R8Pq(x,y)
Note: Radian mode is set.
P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists. P8Rx(r,q), P8Ry(r,q)
TEST (Relational) Operations
TEST Menu To display the TEST menu, press y :.

This operator.

TEST 1: = 2: 3: > 4: 5: < 6: LOGIC

Returns 1 (true) if.

Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to
=, , >, , <, Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists. For = and only, valueA and valueB also can be matrices or complex numbers. If valueA and valueB are matrices, both must have the same dimensions. Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.
TI-83 Plus Math, Angle, and Test Operations 101
valueA=valueB valueA>valueB valueA<valueB
valueAvalueB valueAvalueB valueAvalueB
Using Tests Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1). The expression 2+2=2+3 returns 0. The TI-83 Plus performs the addition first because of EOS rules, and then it compares 4 to 5. The expression 2+(2=2)+3 returns 6. The TI-83 Plus performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.

TI-83 Plus Function Graphing 125

RectGC, PolarGC

RectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinates X and Y. PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R and q.
The RectGC/PolarGC setting determines which variables are updated when you plot the graph, move the free-moving cursor, or trace.
RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed. PolarGC updates X, Y, R, and q; if CoordOn format is selected, R and q
are displayed. CoordOn, CoordOff
CoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If ExprOff format is selected, the function number is
displayed in the top-right corner.
CoordOff (coordinates off) does not display the function number or
GridOff, GridOn Grid points cover the viewing window in rows that correspond to the tick marks on each axis.
GridOff does not display grid points. GridOn displays grid points.

AxesOn, AxesOff

AxesOn displays the axes. AxesOff does not display the axes.
This overrides the LabelOff/ LabelOn format setting. LabelOff, LabelOn
LabelOff and LabelOn determine whether to display labels for the axes (X and Y), if AxesOn format is also selected.

ExprOn, ExprOff

ExprOn and ExprOff determine whether to display the Y= expression
when the trace cursor is active. This format setting also applies to stat plots. When ExprOn is selected, the expression is displayed in the top-left corner of the graph screen. When ExprOff and CoordOn both are selected, the number in the top-right corner specifies which function is being traced.

Displaying Graphs

Displaying a New Graph To display the graph of the selected function or functions, press s. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-83 Plus plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated. Pausing or Stopping a Graph While plotting a graph, you can pause or stop graphing. Press to pause; then press to resume. Press to stop; then press s to redraw.

Smart Graph Smart Graph is a TI-83 Plus feature that redisplays the last graph immediately when you press s, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.
If you performed any of these actions since the graph was last displayed, the TI-83 Plus will replot the graph based on new values when you press s. Changed a mode setting that affects graphs Changed a function in the current picture Selected or deselected a function or stat plot Changed the value of a variable in a selected function Changed a window variable or graph format setting Cleared drawings by selecting ClrDraw Changed a stat plot definition
Overlaying Functions on a Graph On the TI-83 Plus, you can graph one or more new functions without replotting existing functions. For example, store sin(X) to Y1 in the Y= editor and press s. Then store cos(X) to Y2 and press s again. The function Y2 is graphed on top of Y1, the original function.
Graphing a Family of Curves If you enter a list (Chapter 11) as an element in an expression, the TI-83 Plus plots the function for each value in the list, thereby graphing a family of curves. In Simul graphing-order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.
{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X).
{2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X).
Note: When using more than one list, the lists must have the same dimensions.
Exploring Graphs with the Free-Moving Cursor
Free-Moving Cursor When a graph is displayed, press |, ~, }, or to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or , the cursor moves from the center of the viewing window. As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if CoordOn format is selected. The Float/Fix decimal mode setting determines the number of decimal digits displayed for the coordinate values. To display the graph with no cursor and no coordinate values, press or. When you press |, ~, }, or , the cursor moves from the same position. Graphing Accuracy The free-moving cursor moves from pixel to pixel on the screen. When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function. The coordinate
value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r. The coordinate values displayed as you move the cursor approximate actual math coordinates, *accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a Zoom In) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.
Free- moving cursor on the curve

TI-83 Plus Pixels in Horiz and G.T Modes
Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.
DRAW POINTS Menu Pixel Instructions For Pxl.On(, Pxl.Off(, Pxl.Change(, and pxl.Test(: In Horiz mode, row must be {30; column must be {94. In G.T mode, row must be {50; column must be {46.

Pxl.On(row,column)

DRAW Menu Text( Instruction For the Text( instruction: In Horiz mode, row must be {25; column must be {94.

Split Screen 254

In G.T mode, row must be {45; column must be {46.
Text(row,column,"text")
PRGM I/O Menu Output( Instruction For the Output( instruction: In Horiz mode, row must be {4; column must be {16. In G.T mode, row must be {8; column must be {16.
Output(row,column,"text")
Setting a Split-Screen Mode from the Home Screen or a Program To set Horiz or G.T from a program, follow these steps. 1. Press z while the cursor is on a blank line in the program editor. 2. Select Horiz or G.T. The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution.
Note: You also can paste Horiz or G.T to the home screen or program editor from the CATALOG (Chapter 15).

Chapter 10: Matrices

Getting Started: Systems of Linear Equations
Getting Started is a fast-paced introduction. Read the chapter for details. Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-83 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form.
1. Press y >. Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A] 2. Press to define a 24 matrix. The rectangular cursor indicates the current element. Ellipses (.) indicate additional columns beyond the screen. 3. Press 1 to enter the first element. The rectangular cursor moves to the second column of the first row.

Matrices

4. Press 3 to complete the first row for X + 2Y + 3Z = 3. 5. Press to enter the second row for 2X + 3Y + 4Z = 3. 6. Press y 5 to return to the home screen. If necessary, press to clear the home screen. Press y > ~ to display the MATRX MATH menu. Press } to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen. 7. Press y > 1 to select 1: [A] from the MATRX NAMES menu. Press . The reduced row-echelon form of the matrix is displayed and stored in Ans. 1X N 1Z = L3 1Y + 2Z = 3 therefore therefore X = L3 + Z Y = 3 N 2Z

columns.

Matr4list(matrix,listname1,listname2,. ,listname n)
Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specific column from matrix, you must enter a column# after matrix. Matr4list(matrix,column#,listname)
preceding one to five characters identifies those characters as a usercreated listname. listname may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q. listname
Generally, must precede a user-created list name when you enter a user-created list name where other input is valid, for example, on the home screen. Without the , the TI-83 Plus may misinterpret a usercreated list name as implied multiplication of two or more characters.
need not precede a user-created list name where a list name is the only valid input, for example, at the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the stat plot editor. If you enter where it is not necessary, the TI-83 Plus will ignore the entry.

LIST MATH Menu

LIST MATH Menu To display the LIST MATH menu, press y 9 |.
NAMES OPS MATH 1:min( 2:max( 3:mean( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance(
Returns minimum element of a list. Returns maximum element of a list. Returns mean of a list. Returns median of a list. Returns sum of elements in a list. Returns product of elements in list. Returns standard deviation of a list. Returns the variance of a list.
min( (minimum) and max( (maximum) return the smallest or largest element of listA. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. For a complex list, the
element with smallest or largest magnitude (modulus) is returned.
min(listA[,listB]) max(listA[,listB])
Note: min( and max( are the same as min( and max( on the MATH NUM menu.

mean(, median(

mean( returns the mean value of list. median( returns the median value of list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list.
Complex lists are not valid.
mean(list[,freqlist]) median(list[,freqlist])

sum(, prod(

sum( (summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or

Area is the area above the 95th percentile. low is the lower bound. up is the upper bound.

Inferential Stat Editors

Displaying the Inferential Stat Editors When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or intervals input requirements. Below is the inferential stat editor for T-Test.
Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen.
Using an Inferential Stat Editor To use an inferential stat editor, follow these steps. 1. Select a hypothesis test or confidence interval from the STAT TESTS menu. The appropriate editor is displayed. 2. Select Data or Stats input, if the selection is available. The appropriate editor is displayed.
TI-83 Plus Inferential Statistics and Distributions 388
3. Enter real numbers, list names, or expressions for each argument in the editor. 4. Select the alternative hypothesis (, <, or >) against which to test, if the selection is available. 5. Select No or Yes for the Pooled option, if the selection is available. 6. Select Calculate or Draw (when Draw is available) to execute the instruction. When you select Calculate, the results are displayed on the home screen. When you select Draw, the results are displayed in a graph.
This chapter describes the selections in the above steps for each hypothesis test and confidence interval instruction.
Select Data or Stats input
Select an alternative hypothesis Select Calculate or Draw output
Enter values for arguments
Selecting Data or Stats Most inferential stat editors prompt you to select one of two types of input. (1.PropZInt and 2.PropZTest, 1.PropZInt and 2.PropZInt, c2.Test, and LinRegTTest do not.) Select Data to enter the data lists as input. Select Stats to enter summary statistics, such as , Sx, and n, as input.
To select Data or Stats, move the cursor to either Data or Stats, and then press. Entering the Values for Arguments Inferential stat editors require a value for every argument. If you do not know what a particular argument symbol represents, see the Inferential Statistics Input Descriptions tables. When you enter values in any inferential stat editor, the TI-83 Plus stores them in memory so that you can run many tests or intervals without having to reenter every value.
Selecting an Alternative Hypothesis ( < >) Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses. The first is a alternative hypothesis, such as mm0 for the Z.Test. The second is a < alternative hypothesis, such as m1<m2 for the 2.SampTTest. The third is a > alternative hypothesis, such as p1>p2 for the 2.PropZTest.

LISTA={140} LISTB={146} Data Stats
TI-83 Plus Inferential Statistics and Distributions

2.SampTTest

2.SampTTest (two-sample t test; item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.
Ha: m1m2 (m1:m2) Ha: m1<m2 (m1:<m2) Ha: m1>m2 (m1:>m2)
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} Data Stats

1.PropZTest

1.PropZTest (one-proportion z test; item 5) computes a test for an
unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. 1.PropZTest tests the null hypothesis H0: prop=p0 against one of the alternatives below. Ha: propp 0 (prop:p0) Ha: prop<p0 (prop:<p0) Ha: prop>p 0 (prop:>p0)

2.PropZTest

2.PropZTest (two-proportion z test; item 6) computes a test to compare
the proportion of successes (p1 and p2) from two populations. It takes as input the count of successes in each sample (x1 and x2) and the count of observations in each sample (n1 and n2). 2.PropZTest tests the null hypothesis H0: p1=p2 (using the pooled sample proportion ) against one of the alternatives below. Ha: p1p2 (p1:p2) Ha: p1<p2 (p1:<p2) Ha: p1>p2 (p1:>p2)

ZInterval

ZInterval (one-sample z confidence interval; item 7) computes a
confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level. In the example:

TInterval

TInterval (one-sample t confidence interval; item 8) computes a
confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. In the example:
L6={1.6 1.7 1.8 1.9} Data Stats

2.SampZInt

2.SampZInt (two-sample z confidence interval; item 9) computes a
confidence interval for the difference between two population means (m1Nm2) when both population standard deviations ( s1 and s2) are known. The computed confidence interval depends on the user-specified confidence level. In the example:
LISTC={140} LISTD={146} Data Stats

2.SampTInt

2.SampTInt (two-sample t confidence interval; item 0) computes a
confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. The computed confidence interval depends on the userspecified confidence level. In the example:

PLOT You can specify whether you want the calculator to collect realtime (RealTme) samples, which means that the calculator graphs data points immediately as they are being collected, or you can wait and show the graph only after all data points have been collected (End). Highlight the option you want with the cursor keys, and then press. Ymin and Ymax To specify Ymin and Ymax values for the final graph, press p to view the PLOT WINDOW screen. Use $ and # to move between options. Enter Ymin and Ymax using the number keys. Press - l to return to the DATA LOGGER options screen. DIRECTNS (Directions) If DIRECTNS=On, the calculator displays step-by-step directions on the screen, which help you set up and run the data collection. To select On or Off, highlight the one you want with the cursor keys, and then press b. With the Sonic data collection probe, if DIRECTNS=On, the calculator displays a menu screen before starting the application asking you to select 1:CBL or 2:CBR. This ensures that you get the appropriate directions. Press 1 to specify CBL 2/CBL or 2 to specify CBR.
TI-83 Plus Applications 476
Data Collection Results The calculator automatically converts all collected data points into list elements using the following list names (you cannot rename the lists):
Probe Temp Light Volt Sonic Time Values (X) stored to:

TTEMP TLGHT TVOLT TDIST

TEMP LIGHT VOLT DIST
Note: These lists are only temporary placeholders for data results for any particular probe. Therefore, every time you collect data for one of the four probes, the list pertaining to that probe is overwritten with data results from the most recently collected data.
If you want to save data results from more than one data collection, copy all list elements that you want to save to a list with a different name. Also, the GAUGE data collection method stores data results to the same list names, overwriting previously-collected data results, even those collected using the DATA LOGGER data collection method.
TI-83 Plus Applications 477
RANGER Selecting the RANGER data collection method runs the CBR RANGER program, a customized program especially for the TI-83 Plus that makes it compatible with the CBR. When the collection process is halted, the CBR RANGER is deleted from RAM. To run the CBR RANGER program again, press and select the CBL/CBR application.
Note: The Ranger data collection method only uses the Sonic probe.
1. Press b. 2. Select 3:RANGER.

3. Press b.

4. Select options.
For detailed information about the RANGER program as well as option explanations, see the Getting Started with CBR guidebook.
TI-83 Plus Applications 478

Starting Data Collection

Collecting the Data After you specify all of the options for your data collection method, select the Go option from the GAUGE or DATA LOGGER options screen. If you are using the RANGER data collection method, select 1:SETUPSAMPLE from the MAIN menu, and then START NOW. If DIRECTNS=Off, GAUGE and DATA LOGGER data collection begin immediately. If DIRECTNS=On, the calculator displays step-by-step directions.

Tip: To move the cursor to the beginning of a command line, press y |; to move to the end, press y ~. To scroll the cursor down seven command lines, press . To scroll the cursor up seven command lines, press }.
Inserting and Deleting Command Lines To insert a new command line anywhere in the program, place the cursor where you want the new line, press y 6, and then press. A colon indicates a new line. To delete a command line, place the cursor on the line, press to clear all instructions and expressions on the line, and then press { to delete the command line, including the colon.
Copying and Renaming Programs
Copying and Renaming a Program To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating a New Program, and then follow these steps. 1. Press y K. Rcl is displayed on the bottom line of the program editor in the new program (Chapter 1). 2. Press | to display the PRGM EXEC menu. 3. Select a name from the menu. prgmname is pasted to the bottom line of the program editor. 4. Press. All command lines from the selected program are copied into the new program. Copying programs has at least two convenient applications. You can create a template for groups of instructions that you use frequently. You can rename a program by copying its contents into a new program.

Programming 509

Note: You also can copy all the command lines from one existing program to another existing program using RCL.
Scrolling the PRGM EXEC and PRGM EDIT Menus The TI-83 Plus sorts PRGM EXEC and PRGM EDIT menu items automatically into alphanumerical order. Each menu only labels the first 10 items using 1 through 9, then 0. To jump to the first program name that begins with a particular alpha character or q, press [letter from A to Z or q].
Tip: From the top of either the PRGM EXEC or PRGM EDIT menu, press } to move to the bottom. From the bottom, press to move to the top. To scroll the cursor down the menu seven items, press . To scroll the cursor up the menu seven items, press }.
PRGM CTL (Control) Instructions
PRGM CTL Menu To display the PRGM CTL (program control) menu, press from the program editor only.
CTL 1:If 2:Then 3:Else 4:For( 5:While 6:Repeat 7:End 8:Pause 9:Lbl 0:Goto A:IS>( B:DS<( C:Menu( D:prgm E:Return F:Stop G:DelVar H:GraphStyle( TI-83 Plus Programming I/O EXEC
Creates a conditional test. Executes commands when If is true. Executes commands when If is false. Creates an incrementing loop. Creates a conditional loop. Creates a conditional loop. Signifies the end of a block. Pauses program execution. Defines a label. Goes to a label. Increments and skips if greater than. Decrements and skips if less than. Defines menu items and branches. Executes a program as a subroutine. Returns from a subroutine. Stops execution. Deletes a variable from within program. Designates the graph style to be drawn.

11. Press r. After the graph is plotted, press 100 to trace to X=100. Press 150. Press 188. Notice that as X increases, the value of Y converges to p62, which is approximately 113.097. Y2=pB2 (the area of the circle) is a horizontal asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr 2) as N gets large.
Computing and Graphing Mortgage Payments
Problem You are a loan officer at a mortgage company, and you recently closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now. Procedure 1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode settings to the defaults. 2. Press to display the TVM Solver. Enter these values.
Note: Enter a positive number (800) to show PMT as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter 0 for FV,
TI-83 Plus Activities 592
since the future value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the end of a period.
3. Move the cursor onto the PV= prompt, and then press \. The present value, or mortgage amount, of the house is displayed at the PV= prompt.
Now compare the graph of the amount of interest with the graph of the amount of principal for each payment. 4. Press z. Set Par and Simul. 5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown.
Note: GPrn( and GInt( are located on the FINANCE menu (APPS 1:FINANCE).
6. Press p. Set these window variables.
Tmin=1 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=10 Ymin=0 Ymax=1000 Yscl=100
Tip: To increase the graph speed, change Tstep to 24.
7. Press r. After the graph is drawn, press 240 to move the trace cursor to T=240, which is equivalent to 20 years of payments.
The graph shows that for the 240th payment (X=240), 358.03 of the 800 payment is applied to principal (Y=358.03).
Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800.
8. Press to move the cursor onto the function for interest defined by X2T and Y2T. Enter 240.
The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441.97). 9. Press y 5 9 to paste 9:bal( to the home screen. Check the figures from the graph.
At which monthly payment will the principal allocation surpass the interest allocation?
Chapter 18: Memory and Variable Management
Checking Available Memory
MEMORY Menu At any time you can check available memory or manage existing memory by selecting items from the MEMORY menu. To access this menu, press y L.
MEMORY 1:About. 2:Mem Mgmt/Del. 3:Clear Entries 4:ClrAllLists 5:Archive. 6:UnArchive. 7:Reset. 8:Group.

You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example, DrawInv in a graphing mode other than Func.

NO SIGN CHNG

Possible Causes and Suggested Remedies The solve( function or the equation solver did not detect a sign change. You attempted to compute when FV, (PMT), and PV are all 0, or when FV, (PMT), and PV are all 0. You attempted to compute irr( when neither CFList nor CFO is > 0, or when neither CFList nor CFO is < 0.

NONREAL ANS

In Real mode, the result of a calculation yielded a complex result. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph. You attempted to enter, or you have calculated, a number that is beyond the range of the calculator. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph. You attempted to use a system variable inappropriately. See Appendix A. A singular matrix (determinant = 0) is not valid as the argument for L1. The SinReg instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist. This error is not returned during graphing. The TI-83 Plus allows for undefined values on a graph.

OVERFLOW

RESERVED SINGULAR MAT

SINGULARITY

Possible Causes and Suggested Remedies expression in the solve( function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both. You attempted a stat calculation with lists that are not appropriate. Statistical analyses must have at least two data points. Med.Med must have at least three points in each partition. When you use a frequency list, its elements must be 0. (Xmax N Xmin) Xscl must be 47 for a histogram. You attempted to display a graph when a stat plot that uses an undefined list is turned on. The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. See Appendix A and the appropriate chapter. You requested a tolerance to which the algorithm cannot return an accurate result.

STAT PLOT SYNTAX

TOL NOT MET

UNDEFINED

Possible Causes and Suggested Remedies You referenced a variable that is not currently defined. For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as a after Med.Med. Electrical interference caused a link to fail or this calculator is not authorized to run the application. You have tried to archive a variable that cannot be archived or you have have.tried to unarchive an application or group. Examples of variables that cannot be archived include: Real numbers LRESID, R, T, X, Y, Theta, Statistic variables under Vars, STATISTICS menu, Yvars, and the AppIdList.

VALIDATION VARIABLE

VERSION
You have attempted to receive an incompatible variable version from another calculator.

WINDOW RANGE

Possible Causes and Suggested Remedies A problem exists with the window variables. You defined Xmax Xmin or Ymax Ymin. You defined qmax qmin and qstep > 0 (or vice versa). You attempted to define Tstep=0. You defined Tmax Tmin and Tstep > 0 (or vice versa). Window variables are too small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI-83 Pluss numerical range.
A point or a line, instead of a box, is defined in ZBox. A ZOOM operation returned a math error.

Accuracy Information

Computational Accuracy To maximize accuracy, the TI-83 Plus carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a twodigit exponent. You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl, Tstep, and qstep). Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent.
RegEQ displays up to 14 digits in Float mode. Using a fixed-decimal setting other than Float causes RegEQ results to be rounded and
stored with the specified number of decimal places.
Xmin is the center of the leftmost pixel, Xmax is the center of the next-to-
the-rightmost pixel. (The rightmost pixel is reserved for the busy indicator.) @X is the distance between the centers of two adjacent pixels. In Full screen mode, @X is calculated as (Xmax N Xmin) 94. In G.T split-screen mode, @X is calculated as (Xmax N Xmin) 46. If you enter a value for @X from the home screen or a program in Full screen mode, Xmax is calculated as Xmin + @X 94. In G.T splitscreen mode, Xmax is calculated as Xmin + @X 46.

General Information 754

Ymin is the center of the next-to-the-bottom pixel; Ymax is the center of the top pixel. @Y is the distance between the centers of two adjacent pixels.

not equal to (), 101, 694 not( (Boolean operator), 104, 673 nPr (permutations), 93, 673 npv( (net present value), 453, 673 numerical derivative, 70, 152, 165, 175 numerical integral, 70, 153
Omit, 619, 645 ON/HALT, 480
one-proportion z confidence interval (1.PropZInt), 410, 676 one-proportion z test (1.PropZTest), 402, 676 one-sample t confidence interval (TInterval), 406, 687 one-variable statistics (1.Var Stats), 357, 689 or (Boolean) operator, 103, 673 order of evaluating equations, 47 Output(, 255, 530, 673 Overwrite, 619, 645 Overwrite All, 619

P4Rx(, P4Ry(

(polar-to-rectangular conversions), 100, 678 P/Y (number-of-payment-periods-peryear variable), 444, 463
panning, 136 (parametric graphing mode), 23, 674 parametric equations, 159 parametric graphing CALC (calculate operations on a graph), 165 defining and editing, 158, 159 free-moving cursor, 163 graph format, 161 graph styles, 159 moving the cursor to a value, 164 selecting and deselecting, 160 setting parametric mode, 158 tracing, 163 window variables, 160 Y= editor, 158 zoom operations, 165 parentheses, 48 path () graph style, 117 Pause, 518, 674 pausing a graph, 129 Pen, 232 permutations (nPr), 93, 673 phase plots, 197 Pi (p), 66 Pic (pictures), 239 pictures (Pic), 239 pixel, 237 pixels in Horiz/G.T modes, 238, 254

Par/Param 778

PLOT, 476 Plot1(, 373, 674 Plot2(, 373, 674 Plot3(, 373, 674 PlotsOff, 375, 675 PlotsOn, 375, 675
plotting modes, 23 plotting stat data, 368 PMT (payment amount variable), 444, 462 Pmt_Bgn (payment beginning variable), 461, 675 Pmt_End (payment end variable), 461, 675 poissoncdf(, 432, 675 poissonpdf(, 432, 675 Pol/Polar (polar graphing mode), 23, 168, 675 polar equations, 169 polar form, complex numbers, 87 polar graphing CALC (calculate operations on a graph), 175 defining and displaying, 168 equations, 169 free-moving cursor, 173 graph format, 171 graph styles, 169 mode (Pol/Polar), 23, 168, 675 moving the cursor to a value, 174
selecting and deselecting, 169 tracing, 173 window variables, 170 Y= editor, 168 ZOOM operations, 174 PolarGC (polar graphing coordinates), 126, 676 pooled option, 388, 391 power (^), 64, 695 power of ten (10^(), 65, 695 present value, 444, 450 previous entry (Last Entry), 33 prgm (program name), 522, 676 PRGM CTL (program control menu), 511 PRGM EDIT menu, 510 PRGM EXEC menu, 510 PRGM I/O (Input/Output menu), 525 PRGM NEW menu, 500 probability, 92 probability density function (normalpdf(), 425, 673 probe, 468 prod( (product), 313, 676 programming copying and renaming, 509 creating new, 500 defined, 500 deleting, 501 deleting command lines, 508

TI-83 Plus

SILVER EDITION
Addendum to the TI-83 Plus Developer Guide

Beta Version.02

IMPORTANT INFORMATION
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 program. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
2001 Texas Instruments Incorporated
The following information is provided as an addendum to the TI-83 Plus Developer Guide Version 1.0. This text provides additional information for developing applications and assembly programs for the TI-83 Plus SILVER EDITION. Specific information deals with the Flash ROM size and processor speed changes over the TI-83 Plus graphing calculator platform.

OVERVIEW

The TI-83 Plus SILVER EDITION has the capability to load up to 94 Flash Apps and has a clock speed that is more than twice as fast as the standard TI-83 Plus. For compatibility, the TI-83 Plus SILVER EDITION runs programs and applications at the standard TI-83 Plus speed. The TI-83 Plus SILVER EDITION also contains a hardware assist to speed up link communication. Flash Apps can utilize new Operating System (OS) calls or header settings to take advantage of the increased speed. Assembly programs can also use the OS calls to set speed. The new calls will not be recognized by older OSs so it is important for the developer to check OS versions when making these calls.

FLASH ROM STRUCTURE

The TI-83 Plus SILVER EDITION Flash ROM is composed of 2048K (2M) bytes divided into 128 pages, each of which is 16K bytes in size. The structure is generally the same as the TI-83 Plus except for the inclusion of 96 additional 16K pages (24 additional 64K Sectors). The TI-83 Plus SILVER EDITION can store up to 94 Apps in pages 0Ch 69h. The TI-83 Plus Flash structure chart, Figure 2.5 in the TI-83 Plus Developer Guide Version 1.0, is correct up to page 14h; at that point, the TI-83 Plus SILVER EDITION includes more data pages. The TI-83 Plus SILVER EDITION also has the Operating System residing at the high 8 pages of Flash, 78h. 7Fh. The TI-83 Plus high memory is 18h. 1Fh.
TI-83 Plus Developer Guide
Beta Version May 16, 2001
TI-83 Plus SILVER EDITION
Addr OS SWAP/USER DATA SWAP/USER APPS/DATA USER APPS/DATA USER APPS/DATA USER APPS/DATA CERTIFICATE LIST FUTURE OS USE OS Legend SWAP and/or User APPS Area Update System (OS) Area Fixed Area changeable only by TI 00h 07h 08h 0Bh 0Ch 0Fh 10h 13h 14h 67h 68h 69h 6Ah 6Bh 6Ch 77h 78h 7Fh Page(s) Size 128K (8 pages) 64K (4 pages) 64K (4 pages) 64K (4 pages) 1344K (84 pages) 32K (2 pages) 32K (2 pages) 192K (12 pages) 32K (8 pages) Pages 18h. 1Fh on TI-83 Plus Notes Same as TI-83 Plus Same as TI-83 Plus Same as TI-83 Plus Same as TI-83 Plus Many more user pages Pages 14h, 15h on TI-83 Plus Pages 16h, 17h on TI-83 Plus
Because of the additional Flash memory, the first App loaded will be placed at page 69h (105 decimal) and downward from there (versus 15h for the TI-83 Plus).
ENTRY POINTS, VARIABLE TYPES, AND SYSTEM FLAGS
The TI-83 Plus SILVER EDITION uses the same entry points, variable types, and system flags as the TI-83 Plus.
ADDITIONAL B_CALLS FOR DETERMINING OS AND SPEED
The TI-83 Plus SILVER EDITION and TI-83 Plus OS version 1.13 includes new B_CALL entry points that allow an application to set the processor speed (SetExSpeed) and to determine the current speed and OS (GetSysInfo). The ti83plus.inc has the following entries:
SetExSpeed GetSysInfo NzIf83Plus EQU EQU EQU 50BFh 50DDh 50E0h
See the entry point documentation in Appendix A for additional information.
ADDITIONAL HEADER TAGS FOR SETTING SPEED
By default, an application will run at the TI-83 Plus Speed unless the App informs the OS to allow it to run faster. The entry point SetExSpeed controls specific locations in the code. An optional method is to set a tag in the header that informs the OS that the App can run at a certain level. The default level is 0 and the TI-83 Plus SILVER EDITION can be set to level 1. The APP_HW_LEVEL tag looks as follows:

DB DB 080h,0A1h 001h ; Field: App level ; Highest HW level = 1
If this field is missing or is set to HW level 0 (either DB 080h,0A0h or DB 080h,0A1h,000h), then the Operating System executes the App in slow mode (6MHz) to execute the App. This field is ignored on the TI-83 Plus.
; This is the application header definition area required for all Apps. ; Field: Program length ; Length = 0 (N/A for unsigned ; Apps) -----------------------------------------------------------------------------* * * App types * * * This example uses shareware type for signing and the simulator. Replace with the commented developer ID for debugging on the calculator. Note the header will need to be adjusted depending on the number of bytes in this type field. -----------------------------------------------------------------------------DB 080h, 012h ; Field: Program type (2 byte) DB 001h, 004h ; Type = Shareware, TI-83 Plus ------------------------------; Use with 5 or 6 character ID DB 080h, 013h ; Field: Program type (3 byte) DB 001h, 07Fh, 004h ; Dev. ID = "17F04" -----------------------------------------------------------------------------DB 080h, 021h ; Field: App ID DB 001h ; Id = 1 DB 080h, 031h ; Field: App Build DB 001h ; Build = 1 ------------------------------------------------------------------------------- App Name is to be 8 characters in size -DB 080h, 048h ; Field: App Name DB "TEMPxxxx" ; Name = "TEMP " DB 080h, 081h ; Field: App Pages DB 001h ; App Pages = 1 DB 080h, 090h ; No default splash screen -----------------------------------------------------------------------------DB 080h, 0A1h ; Field: App level DB 001h ; Highest HW level = 1 -----------------------------------------------------------------------------DB 003h, 026h, 009h, 004h ; Field: Date stamp = DB DB 080h, 00Fh 000h, 000h, 000h, 000h

; ; ; ; ; ; ;

; ; ; ; ;
DB 005h, 0D4h, 062h, 000h ; 2/7/2000 DB 002h, 00Dh, 040h ; Dummy encrypted TI date DB 055h, 073h, 021h, 0E3h ; stamp signature DB 03Bh, 081h, 022h, 017h DB 02Dh, 0D2h, 0D3h, 018h DB 093h, 063h, 078h, 0A6h DB 0A2h, 006h, 05Ch, 071h DB 0C0h, 031h, 0E5h, 098h DB 0DEh, 06Dh, 039h, 03Ch DB 0F8h, 035h, 0E0h, 0A7h DB 00Fh, 092h, 0A5h, 037h DB 068h, 0F3h, 040h, 019h DB 06Eh, 0CAh, 02Fh, 064h DB 0E9h, 0AAh, 0CFh, 0C9h DB 035h, 039h, 0C0h, 043h DB 05Bh, 0D3h, 037h, 086h DB 041h, 0E2h, 001h, 090h -----------------------------------------------------------------------------DB 080h, 07Fh ; Field: Program Image length DB 000h, 000h, 000h, 000h ; Length = 0, N/A -----------------------------------------------------------------------------End of required Header. To allow for growth of header fields during the signing process, the following pad bytes are needed. Adjust as needed. DB 0, 0, 0, 0 ; Reserved Pad DB 0, 0, 0, 0 ; Reserved Pad DB 0, 0, 0, 0 ; Reserved Pad DB 0 ; Adjusted pad for level type -----------------------------------------------------------------------------Adjust header according to application type. This example uses shareware type (2-bytes). Replace with the commented pads if using a 3-byte developer ID. DB 0, 0, 0, 0 ; Reserved bytes with pad for ; 2-byte Program Type field DB 0, 0, 0 ; Reserved bytes with pad for ; 3-byte Program Type field

; ; ; ;

; ; End of 128 byte application header ; -----------------------------------------------------------------------------; ; Execution starts here.
POSSIBLE DISPLAY PROBLEMS RUNNING FAST ON THE SILVER EDITION
There are problems that can occur if an application that was written for the TI-83 Plus is run at fast speed on the TI-83 Plus Silver Edition. The screen may not display correctly if the app writes directly to the display and has its own version of LCD_BUSY instead of calling the system routine. The LCD has a delay requirement of approximately 10us between operations and using the old LCD_BUSY delay at the faster speed will be less than this.
There are three options for solving this problem. Triple or quadruple the delay time of the in-line code. This will solve the problem, but it may reoccur if another even faster version is produced. Do B_CALL LCD_BUSY. This is guaranteed to work, but may slow down a display intensive app. Use a CALL LCD_BUSY_QUICK, where LCD_BUSY_QUICK is equated to 000Bh. This is a new entry point that does not require the system overhead of a B_CALL. This call also works on earlier TI-83 Plus versions, but runs slightly faster than 10us and modifies the z/nz Status Flag. To use this on all versions, wrap it in another routine that saves and restores the flag register:
PUSH CALL POP AF LCD_BUSY_QUICK AF ; 11 states ; 17 states + 30 states (on TI-83 Plus) ; 10 states
This will ensure that the routine runs on both the TI-83 Plus and the TI-83 Plus Silver Edition with minimal additional time delays.
ACCESSING THE DBUS FROM AN APP
The TI-83 Plus SILVER EDITION is equipped with a DBUS assist unit in the hardware. This hardware assist will greatly speed up Apps that do significant DBUS activity, but requires additional care on the part of the App programmer. When used incorrectly, the DBUS assist will cause the App to suffer from timeout errors even though the data is sent/received correctly. The paragraphs below provide several use scenarios, possible problems encountered, and possible fixes.
Monitoring DBUS Lines to Detect DBUS Activity
Frequently, an App will need to wait for a byte to be sent from another calculator while the App is in a loop doing something else. On the TI-83 Plus, it was standard practice to input the state of the DBUS lines on each pass through the loop and then to make a B_CALL to RecAByte ONLY when one of the DBUS lines was active (a low). With the hardware assist, this process will fail. The failure is due to the fact that the hardware assist will complete the handshake when the DBUS line goes active by reading in the incoming byte and storing the byte in a hardware buffer. Thus the DBUS lines will return to an inactive state in a few microseconds and the software will never detect any activity. The corrective action here is to first determine the type of hardware that the App is being executed on by calling the GetSysInfo utility. If the hardware type indicates a TI-83 Plus SILVER EDITION unit (e.g., Bit 03 is set), then activity on the DBUS lines must be determined by executing the following code:

IN AND (0x09), A 0x38

If the nz bit is set, the DBUS hardware assist has stored a byte for retrieval OR IS IN THE PROCESS OF RECEIVING A BYTE AT THE PRESENT TIME. This is the only reliable way of determining activity on the DBUS on the TI-83 Plus SILVER EDITION hardware.
Sending DBUS Data/Error States by Toggling the DBUS Lines
Frequently Apps will attempt to flag an error to the DBUS by taking both DBUS lines low. Similarly, Apps may attempt to toggle the DBUS lines from within the App rather than by invoking the RecAByte and SendAByte routines. These actions will cause the DBUS hardware assist to reset each time either (or both) of the DBUS lines are placed into the low state. If the DBUS assist hardware is in the middle of a transmission when the App toggles the DBUS line, the transaction is aborted and the byte being sent or received is lost.
Unexpected Error Conditions
If the DBUS hardware assist unit is sending data to a DBUS device and that device asserts both DBUS lines low, the DBUS assist will abort the send with an error condition. The indicated error will be TIMEOUT, as the hardware will only know that it could not send the byte in the 2 seconds allotted.

Summary

In general, it is always safe to call RecAByte and SendAByte. Direct access to the DBUS lines is discouraged as it may cause communication problems.
Appendix A: System Routines Utility

GetSysInfo

Category: Description: Input: Registers: HL = RAM location of where to put system information Flags: Others: Outputs: Registers: None Flags: Others: Registers destroyed: Remarks: None (HL). (HL + 8) set depending on system information. AF, BC, HL Note that this B_CALL is not available on TI-83 Plus version 1.12 and earlier. The calling routine needs to check the software version before performing the B_CALL. This routine returns nine bytes representing various aspects of system operation: Byte= = = = = = = = = = Boot Code Revision # (Major) Boot Code Revision # (Minor) Hardware Revision # (00 if TI-83 Plus, NZ if not) Lsn = Current Speed Bit 4 = reset if TI-83 Plus, set if TI-83 Plus SILVER EDITION Device code default 0 = reserved for future use 0 = reserved for future use 0 = reserved for future use 0 = reserved for future use None None Utility Return nine bytes of system information, including current speed.

(continued)

GetSysInfo (continued)
Example: Determine if are running fast or slow:
B_CALL CP JR CP JR LD CP JR MustBeSlow: XOR JR above112: LD B_CALL LD AND Done:. HL,OP1 GetSysInfo A,OP1+3 0Fh A Done ; set Z to show slow ; later than version 1.12 getBaseVer 2 NC,aboveNZ,MustBeSlow A,B 13 NC,above112 ; OS version in (A, B) ; major version ; if 2.x than > 1.12 ; ; ; ; if 0.x then < 1.12 major version is 1 minor version C if minor version < 13
TI-83 Plus Devleoper Guide

NzIf83Plus

Category: Description: Input: Registers: None Flags: Others: Outputs: Registers: None Flags: Others: Registers destroyed: Remarks: NZ = Status if calculator is a TI-83 Plus Z = Status if calculator is a TI-83 Plus SILVER EDITION None None Note that this B_CALL is not available on Cerebrus version 1.12 and earlier. The calling routine needs to check the software version before performing the B_CALL. This routine is not as intrusive as GetSysInfo if all you need to know is if the calculator is an earlier edition of the TI-83 Plus. Example: Return NZ if are running on a TI-83 Plus.
B_CALL CP JR JR LD CP JR MustBe83Plus: RET above112: B_CALL RET NzIf83Plus ; NZ status ; later than version 1.12 ; NZ if original TI-83 Plus getBaseVer 1 C,MustBe83Plus NZ,Above112 A,B 13 NC,above112 ; ; ; ; ; ; ; OS version in (A, B) major version if 0.x than < 1.13 if 2.x then > 1.12 major version is 1 minor version C if minor version < 13
Utility Return status if calculator is a TI-83 Plus or not.

None None

SetExSpeed
Category: Description: Input: Registers: A = 0 to set slow speed (6MHz) A = 1 to set 15MHz A = FF to set Fastest Future speed Flags: Others: Outputs: Registers: None Flags: Others: Registers destroyed: Remarks: None None Flag register modified. Note that this B_CALL is not available on TI-83 Plus version 1.12 and earlier. The calling routine needs to check the software version before performing the B_CALL. This routine can be called on a TI-83 Plus unit running software version 1.13 or higher, but will not affect the operating speed of that unit. The operating system will set the speed back to fast once the app or assembly program returns regardless of any settings made. An exception to this is that the error handler will leave the speed setting as is in case a goto is desired. Some system routines such as the IO utilities may set slow speed for certain operations. These routines will restore the current speed upon completion. Other routines, such as the JForceCmd instruction force the fast clock. Normally an app will not execute these routines except upon completion. None None Utility Set execution speed to fast or slow.

SetExSpeed (continued)

Example: Determine if the app is running on operating system version 1.13 or higher and if so, run at the fast clock frequency:
B_CALL CP JR CP JR LD CP JR above112: LD B_CALL below112:. A,0FFh SetExSpeed ; set fastest speed possible getBaseVer 2 NC,aboveNZ,below112 A,B 13 C,below112 ; ; ; ; ; ; ; ; ; operating system version in (A, B) major version if 2.x then > 1.12 if 0.x then < 1.12 major version is 1 minor version C if minor version < 13 later than version 1.12