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TI-89 - Cengage Learning

1. 5 158 0 3 42 4 Likewise set ymax ymin 98 Ay if you want the vertical increment to be some special Ay would calculate the size of each jump to be Ax Sometimes you may want the jumps to be Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 15 To center your window around a particular point say h k and also have a certain Ax set xmin h 79 Ax and make xmax h 79 Ax Likewise make ymin k 49 Ay and make ymax k 49 Ay For example to center a window around the origin 0 0 with both horizontal and vertical increments of 0 25 set the range so that xmin 0 79 0 25 19 75 xmax 0 79 0 25 19 75 ymin 0 49 0 25 12 25 and ymax 0 49 0 25 12 25 See the benefit by first graphing y x 2x 1 in a standard viewing window Trace near its y intercept which is 0 1 and move towards its x intercept which is 1 0 Then press F2 4 ZoomDec and trace again near the intercepts IV 2 6 Zoom Plot again the two graphs for y x 4x and y 25x There appears to be an intersection near x 2 The TI 89 provides several ways to enlarge the view around this point You can change the viewing window directly by pressing KA WINDOW and editing the values of xmin xmax ymin and ymax Figure V 42 shows a new viewing window for the range displayed in Figure I V 41 The cursor has been moved near the point of intersection
2. Figure IV 107 Sum IV 9 5 Statistics The following data are the high temperatures in degrees Fahrenheit recorded in Lincoln Nebraska from October 1 2003 to October 12 2003 Source University of Nebraska Lincoln 65 68 74 79 83 81 80 80 79 72 67 71 To find the mean and median of these temperatures first enter the data using the TI 89 s list editor Press APPS 6 3 3 Ka aa T EMP S ENTER ENTER to open a new variable called TEMPS see Figure IV 108 Now begin entering the temperatures as shown in Figure IV 109 Then press 2nd QUIT To find the mean press 2nd MATH 6 Statistics 4 mean 2nd a lock T E M P S alpha ENTER and to find the median press 2nd MATH 6 7 median 2nd a lock T E MP S alpha ENTER see Figure IV 110 So the mean of the temperatures is approximately 75 F and the median is 76 5 F F F Cell Fe lok Setur oo es ee T F Folder VOriab Te Rape dieting faidnecuive E ESC CANCEL TYFE CEMTERI OK AAD CESCI CAMCEL RAD AFF RON FOL Figure IV 108 Entering a new variable Figure IV 109 List editor Fir Fer Fo For Too Alebraycatec Clean Ur E peant tenps r4 JI66666 7 E pegdiani tenps re HAIN RAD AFFROH FOL FEN Figure IV 110 Mean and median You can also find the mean and median of the above data by using the OneVar command found in the Calc menu of the Data Matrix Editor You can copy the data you entered in Figure IV 108 to a data list by opening the TEMPS lis
3. by Houghton Mifflin Company All rights reserved 10 Fiz F F4 Fr Taos Trace Reararh Fen 10 RAD AFFERO FURL 10 Figure IV 59 Graph of y x 1 and tangent line atx 1 TI 89 Graphics Calculator IV 3 Solving Equations and Inequalities IV 3 1 Intercepts and Intersections Tracing and zooming are also used to locate an x intercept of a graph where a curve crosses the x axis For example the graph of y x 8x crosses the x axis three times see Figure IV 60 After tracing over to the x intercept point that is farthest to the left zoom in Figure IV 61 Continue this process until you have located all three intercepts with as much accuracy as you need The three x intercepts of y x 8x are approximately 2 828 0 and 2 828 2 5 10 Fir F F4 Fr Fir F3 F4 Fr Tools Trdce Reararh Fen Taos Trace Reararh Fen 10 10 5 41 0 41 mor 2 911392 uci RAD ARFRON FUNC RAD AFFRON FUNC 10 A Figure IV 60 Graph of y x 8x Figure IV 61 Near an x intercept of y x 8x Technology Tip As you zoom in you may also wish to change the spacing between tick marks on the x axis so that the viewing window shows scale marks near the intercept point Then the accuracy of your approximation will be such that the error is less than the distance between two tick marks Change the x scale on the TI 89 from the WINDOW menu Move the cursor down to xscl and enter an appropriate value The x interce
4. Fer For For Too Ts Alebraycate Clean Ur i 2 S 4t 5 Gt 7 Sath 21 12t 34 56 HAIN RAD AFPRON FUNC EEN Figure IV 5 Editing a calculation Technology Tip The TI 89 has two different inputting modes insert and overtype The default mode is insert mode in which the cursor is a blinking vertical line and new text will be inserted at the cursor s position and other characters are pushed to the right In the overtype mode the cursor is a blinking square and the characters that you type replace the existing characters To change from one mode to another press 2nd INS The TI 89 remains in whatever the last input mode was even after being turned off IV 2 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator Even if you had pressed ENTER you may still edit the previous expression Immediately after you press ENTER your entry remains on the entry line Pressing moves the cursor to the beginning of the line while pressing gt puts the cursor at the end of the line Now the expression can be edited as above To edit a previous expression that is no longer on the entry line press 2nd and then ENTRY to recall the prior expression Now you can change it In fact the TI 89 retains as many entries as the current history area holds in a last entry storage area including entries that have scrolled off the screen Press 2nd ENTRY repeatedly until the previous line you want is on the entry line The
5. Figure IV 47 Before a zoom in Figure IV 48 After a zoom in Mote 253165 yor 9263156 HARIH RAD AFFERO FUNE As you see in the Zoom menu Figure IV 43 the TI 89 can zoom in press F2 2 or zoom out press F2 3 Zoom out to see a larger view of the graph centered at the cursor position You can change the horizontal and vertical scale of the magnification by pressing F2 alpha C SetFactors see Figure IV 49 and editing xFact and yFact the horizontal and vertical magnification factors The ZFact is only used when dealing with three dimensional graphs Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 17 rosis zoom trace Resraph tath trau Penf Fac a ePack Ho zFact Enter O0k E gt C CAMCEL RAD AFFRON FURL Figure IV 49 ZOOM FACTORS menu The default zoom factor is 4 in both directions It is not necessary for xFact and yFact to be equal Sometimes you may prefer to zoom in one direction only so the other factor should be set to 1 Press ESC to leave the ZOOM FACTORS menu and go back to the graph Pressing 2nd QUIT will take you back to the home screen Technology Tip The TI 89 remembers the window it displayed before a zoom So if you should zoom in too much and lose the curve press F2 aloha B Memory 1 ZoomPrev to go back to the window before If you want to execute a series of zooms but then return to a particular window press F2 aloha B 2 ZoomSto to store
6. You can create as many list names as your TI 89 memory has space to store Before entering this new data clear the data in the lists that you want to use To delete a list press 2nd VAR LINK This will display a list of folders showing the variables defined in each folder Highlight the name of the list that you wish to delete and press F1 Manage 1 Delete ENTER The TI 89 will ask you to confirm the deletion by pressing ENTER once more Now press APPS 6 Data Matrix Editor 3 New Ka Ka P R I Z E ENTER to open a new variable called PRIZE Figure IV 73 Press ENTER to then begin entering the variable values with the years going in column C1 Instead of entering the full year let x 5 represent 1995 x 6 represent 1996 and so on Here are the keystrokes for the first three years 5 ENTER 6 ENTER 7 ENTER and so on then press gt to move to the next list Move up to the first row and press 8 06 ENTER 8 11 ENTER 8 61 ENTER and so on see Figure IV 74 Fir F F4 FE Fr Too 1s F Cel Header Cale Egt Fe Tok Serur a ee ee TYPE Fodder JFET Tepe ie thgMi pandengen E ESCSCANCEL TYFE LEMTERI Z0OK AMD CE2CJ CANCEL RAD AFFERO FUNC Figure IV 73 Entering a new variable Figure IV 74 Entering data points IV 26 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator You may edit statistical data in almost the same way you edit expressions in the home screen will delete the entire cell
7. l RAD AFFERO FUNC HAIN RAD AFFERO FUNC Figure IV 80 Data Matrix Editor Figure IV 81 Editing a matrix IV 28 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator The display will show the matrix as a grid with zeros in the rows and columns specified in the definition of the matrix Use the cursor pad or press ENTER repeatedly to move the cursor to a matrix element you want to change If you press ENTER you will move right across a row and then back to the first column of the next row The lower left of the screen shows the cursor s current location within the matrix The element in the second row and first column in Figure IV 81 is highlighted so the lower left of the window is r2c1 1 showing that element s current value Enter all the elements of matrix a pressing ENTER after entering each value When you are finished leave the matrix editing screen by pressing 2nd QUIT or HOME to return to the home screen IV 6 2 Matrix Math From the home screen you can perform many calculations with matrices To see matrix a press aloha A ENTER Figure IV 82 Perform the scalar multiplication 2a by pressing 2 aloha A ENTER The resulting matrix is displayed on the screen To create matrix b as 2a press 2 aloha A STO gt alpha B ENTER Figure IV 83 or if you do this immediately after calculating 2a press only STO gt alpha B ENTER The calculator will display the matrix Fir Fer For For Fir
8. 75 Plot 1 menu Figure IV 76 Scatter plot To draw the scatter plot in a window adjusted automatically to include all the data you entered press F2 9 ZoomData When you no longer want to see the scatter plot press APPS 6 1 Current F2 highlight Plot 1 and use F4 VY to deselect Plot 1 or press K Y move the cursor up to highlight Plot 1 and press F4 v The TI 89 still retains all the data you entered IV 5 3 Regression Line The TI 89 calculates slope and y intercept for the line that best fits all the data After the data points have been entered while still in the Data Matrix Editor press F5 Calc For the Calculation Type choose 5 LinReg and set the x variable to c1 and the y variable to C2 In order to have the TI 89 graph the regression equation set Store RegEQ to as y1 x as shown in Figure IV 77 Press ENTER and the TI 89 will calculate a linear regression model with the slope named a and the y intercept named b Figure IV 78 The correlation coefficient Corr measures how well the linear regression equation fits with the data The closer the absolute value of the correlation coefficient is to 1 the better the fit the closer the absolute value of the correlation coefficient is to 0 the worse the fit The TI 89 displays both the correlation coefficient and the coefficient of determination R Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 27 MmainseFize Calculate i Calc
9. FUNC Figure IV 10 Complex number calculations The TI 89 can also solve for the real and complex solutions of an equation This is done by using the cSolve function which is found in the Algebra sub menu of the MATH menu The format of cSolve is cSolve expression variable For example to find the zeros of f x xX 4x 14x 20 press 2nd MATH 9 Algebra alpha A Complex 1 cSolve To complete the computation press X 3 4 X 2 14X 20 0 X ENTER The TI 89 will display real and complex solutions of the equation as shown in Figure IV 11 Fir Fer For For Too T A Ebr ala de Clean Ur scSolvelx 7 4x2 i4 x 2h x 3 4 of x 3 PF wee i a E e a E deaa D E D a RAD AFFERO FUNE Figure IV 11 cSolve function Note that this calculation and the answer are too long for both the entry line and the history area You can scroll through the entire calculation or answer by using FN or kd to put the cursor on the appropriate line and then using Plor gt to move the cursor to the part of the calculation or answer that you wish to see IV 2 Functions and Graphs IV 2 1 Evaluating Functions Suppose you receive a monthly salary of 1975 plus a commission of 10 of sales Let x your sales in dollars then your wages W in dollars are given by the equation W 1975 10x If your January sales were 2230 and your February sales were 1865 what was your income during those months Here s one method to
10. Fer For For Tao TSAI ebr acae Clean Ur Tao TSAI ebrapla de Clean Ur a ath aie RAD AFF RON FUNC RAD AFFRON FUNC 1 s0 Figure IV 82 Matrix a Figure IV 83 Matrix b To add two matrices say a and b create b with the same dimensions as a and then press aloha A alpha B ENTER Subtraction is performed in a similar manner 3 lL gt i multiplication of c by a press alpha C x alpha A ENTER If you tried to multiply a by c your TI 89 would notify you of an error because the dimensions of the two matrices do not permit multiplication in this way Now create a matrix called c with dimensions of 2 x 3 and enter the matrix as C For matrix IV 6 3 Row Operations Here are the keystrokes necessary to perform elementary row operations on a matrix Your textbook provides a more careful explanation of the elementary row operations and their uses To interchange the second and third rows of the matrix that was defined in Figure IV 82 press 2nd MATH 4 Matrix alpha J Row ops 1 rowSwap alpha A 2 3 ENTER see Figure IV 84 The format of this command is rowSwap matrixl index1 index2 To add row 2 and row 3 and store the results in row 3 press 2nd MATH 4 alpha J 2 rowAdd alpha A 2 3 ENTER The format of this command is rowAdd matrixl index index2 To multiply row 2 by 4 and store the results in row 2 thereby replacing row 2 with new values press 2nd MATH 4 alpha J 3 mRow 4 alpha A 2 ENTER
11. The format of this command is mRow expression matrix index Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 29 Fir Fer For For Fir Fer For For Tao T A Ebr apa de Clean Ur Taos Al ebrapla de Clean Ur Browswapla Z 3 BmRowAdd 4 4a 2 3 i a n i per Sa 6 If rowswapt a 23 mMRowAdd 4 3 22 52 RAD AFFRON FUNC RAD AFFRON FUNC REL Figure IV 84 Interchange rows 2 and 3 Figure IV 85 Add 4 times row 2 to row 3 To multiply row 2 by 4 and add the results to row 3 thereby replacing row 3 with new values press 2nd MATH 4 alpha J 4 mRowAdd 4 aloha A 2 3 ENTER see Figure IV 85 The format of this command is mRowAdd expression matrix index1 index2 Technology Tip Note that your TI 89 does not store a matrix obtained as the result of any row operations So when you need to perform several row operations in succession it is a good idea to store the result of each one in a temporary place x 2y 3z 9 For example use row operations to solve this system of linear equations 4 x 3y 4 2x Sy 5z 17 1 2 3 9 First enter this augmented matrix as a in your TI 89 1 3 O 4 Then return to the home 2 5 5 17 screen and store this matrix as e press aloha A STO gt aloha E ENTER so you may keep the original in case you need to recall it Here are the row operations and their associated keystrokes At each step the result is st
12. This me that both functions will be graphed as shown in Figure IV 38 In the Y screen move the cursor onto y1 and press F4 y The checkmark left of y1 should disappear Figure IV 39 Now press KA GRAPH and see that only y2 is plotted Figure IV 40 10 Fir F F4 Fr Taos Trdce Redraorh Fen 10 TERIAREN HAIN RAD APFRO FUNC RAD APFROR FUNC 10 Figure IV 39 Only y2 active Figure IV 40 Graph of y 25x Many different functions can be stored in the Y list and any combination of them may be graphed simultaneously You can make a function active or inactive for graphing by pressing F4 when the function is highlighted to add a checkmark activate or remove the checkmark deactivate Now go back to the Y screen and do what is needed in order to graph y1 but not y2 Now activate both functions so that both graphs are plotted Press F3 and the cursor appears first on the graph of y x 4x because it is higher up on the Y list You know that the cursor is on this function y1 because of the numeral 1 that is displayed in the upper right corner of the screen Press the up ZN or down B4 direction to move the cursor vertically to the graph of y 25x Now the numeral 2 is displayed in the upper right corner of the screen Next press the left and right arrow keys to trace along the graph of y 25x When more than one function is plotted you can move the trace cursor vertically from one graph to another with the
13. as easily as it plots functions In the first page of the MODE menu Figure IV 1 change the Graph Setting to PARAMETRIC Be sure if the independent parameter is an angle measure that the angle measure in the MODE menu is set to whichever you need RADIAN or DEGREE IV 34 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator For example here are the keystrokes needed to graph the parametric equations x cos and y sin t First check that angles are currently being measured in radians and change to parametric mode Then press K3 Y 2nd COST 3 ENTER 2nd SINT 3 ENTER Figure IV 97 a aM HtLICbi Csintbaa 3 HAIN RAD AFFROS FAR RAD AFFROS FAR Figure IV 97 Parametric Y menu Figure IV 98 Parametric WINDOW menu Press K WINDOW to set the graphing window and to initialize the values of t In the standard window the values of t go from 0 to 277 in steps of a 0 1309 with the view from 10 to 10 in both directions In order to provide a better viewing window press ENTER three times to move the cursor down and set the window to extend from 2 to 2 in both directions Figure IV 98 Press KA GRAPH to see the parametric graph Figure IV 99 2 Fiz F F4 Fr Taos Trace Reararh Fen KAD AFPRON FAR 2 Figure IV 99 Parametric graph of x cos t and y sin t You may zoom and trace along parametric graphs just as you did with function graphs However unlike with functio
14. graph a trigonometric function you need to pay careful attention to the choice of graph window and to your angle measure configuration For example graph sin 30x es 39 in the standard viewing window in radian mode Trace along the curve to see where it is Zoom in to a better window or use the period and amplitude to establish better WINDOW values Technology Tip Because m 3 1 when in radian mode set xmin 0 and xmax 6 3 to cover the interval from 0 to 277 Next graph y tan x in the standard window first then press F2 7 Zoom Trig to change to a special window for trigonometric functions in which the xscl is gt 1 5708 or 90 and the vertical range is from 4 to 4 The TI 89 plots consecutive points and then connects them with a segment so the graph is not exactly what you should expect You may wish to change the plot style from Line to Dot see Section IV 2 3 when you plot the tangent function IV 5 Scatter Plots IV 5 1 Entering Data The table shows the total prize money in millions of dollars awarded at the Indianapolis 500 race from 1995 to 2003 Source Indy Racing League 1995 1996 1997 1998 1999 2000 2001 2002 2003 Prize in millions 8 06 8 11 8 61 8 72 9 05 9 48 9 61 10 03 10 15 We ll now use the TI 89 to construct a scatter plot that represents these points and to find a linear model that approximates the given data The TI 89 holds data in lists
15. need to interrupt a program during execution press ON The instruction manual for your TI 89 gives detailed information about programming Refer to it to learn more about programming and how to use other features of your calculator IV 40 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator
16. number of entries that the history area can hold may be changed see your user s manual for more information To clear the entry line press CLEAR while the cursor is on that line To clear previous entry answer pairs from the history area use PN or Kd to move the cursor to either the entry or the answer and press CLEAR both the entry and the answer will be deleted from the display To clear the entire history area press F1 Tools 8 Clear Home although this will not clear the entry line Technology Tip When you need to evaluate a formula for different values of a variable use the editing feature to simplify the process For example suppose you want to find the balance in an investment account if there is now 5000 in the account and interest is compounded annually at the rate of 8 5 The formula r nt for the balance is P r where P principal r rate of interest expressed as a decimal n n number of times interest is compounded each year and t number of years In our example this becomes 5000 1 085 Here are the keystrokes for finding the balance after t 3 5 and 10 years results are shown in Figure IV 6 Years Keystrokes Balance 3 5000 1 085 3 ENTER 6386 45 5 Jee 5 ENTER 7518 28 10 J m 10 ENTER 11 304 92 Fir Fer Fz For reoisjansebral aiclather ersomm erean ue 6356 445625 a 5000 1 085 7518 283451 s 5000 1 085 1f 11304 91721 RAD AFFERO FOL Figure IV 6
17. rectangular coordinates x y press 2nd MATH 2 3 P gt Rx 3 2nd r ENTER to display the x coordinate Now press 2nd MATH 2 4 P gt Ry 3 2nd m ENTER to display the y coordinate see Figure IV 101 IV 8 3 Graphing Polar Equations The TI 89 graphs polar functions in the form r f 0 In the Graph line of the first page of the MODE menu select POLAR for polar graphs You may now graph up to 99 polar functions at one time Be sure that the angle measure has been set to whichever you need RADIAN or DEGREE Here we will use radian measure For example to graph r 4 sin 0 press KA Y for the polar graph editing screen Then enter the expression 4 sin 0 for r1 by pressing 4 2nd SIN K3 6 ENTER see Figure IV 102 The 6 function is located to the right of the key Choose a good viewing window and an appropriate interval and increment for 0 In Figure IV 103 the viewing window is roughly square and extends from 12 to 12 horizontally and from 6 to 6 vertically Figure IV 103 shows rectangular coordinates of the cursor s location on the graph You may sometimes wish to trace along the curve and see polar coordinates of the cursor s location The first line of the Graph Format menu Figure IV 25 has options for displaying the cursor s position in rectangular RECT or polar POLAR form 6 Fir F F4 Fr Taos Trace Redraorh Fen 1 12 12 Aor 2 So98rs MOL PS40S08 ucil RAD APFRON FOL RAD APFROA FOL 6 F
18. see a graph that appears more circular Technology Tip Another way to get a square graph is to change the range variables so that the value of ymax ymin is approximately 38 times xmax xmin For example see the WINDOW in Figure IV 33 to get the corresponding graph in Figure IV 34 This method works because the dimensions of the TI 89 s display are such that the ratio of vertical to horizontal is approximately ni 9 5 Fir F3 F4 Fr Tools Trace Re3rarh Fen 19 75 RAD AFFERO FUNC RAD APFRO FUNC o vertical 19 _ 38 sure ea horizontal 39 5 79 Figure IV 34 A square circle The two semicircles in Figure V 34 do not connect because of an idiosyncrasy in the way the TI 89 plots a graph Back when you entered V36 x as y2 you could have entered y1 as y2 and saved some keystrokes Try this by going into the Y screen and pressing PN to move the cursor up to y2 Then press CLEAR Y 1 X ENTER The graph should be as before Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 13 IV 2 5 Trace Graph the function y x 4x from Section IV 2 2 using the standard viewing window Remember to clear any other functions in the Y screen Press any of the cursor directions PN Dad and see the cursor move from the center of the viewing window The coordinates of the cursor s location are displayed at the bottom of the screen as in Figure V 35 in floating decimal f
19. the arrow keys to scroll in order to see a long calculation For example type this sum Figure IV 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Then press ENTER to see the answer The sum is too long for both the entry line and the history area The direction s in which the line extends off the screen is indicated by an ellipsis at the end of the entry line and arrows 4 or g in the history area You can scroll through the entire calculation by using FN or kd to put the cursor on the appropriate line and then using 4 or gt to move the cursor to the part of the calculation that you wish to see Fir Fer F F For Too s Alebraycate Clean Ur i 2 S 4t 5 Gt 7 Sath 21 ae ae ee Ti ee i ae EAn RAD AFFERO FURL Figure IV 4 Home screen Often we do not notice a mistake until we see how unreasonable an answer is The TI 89 permits you to redisplay an entire calculation edit it easily then execute the corrected calculation Suppose you had typed 12 34 56 as in Figure IV 5 but had not yet pressed ENTER when you realize that 34 should have been 74 Simply press 4 as many times as necessary to move the blinking cursor line until it is to the immediate right of the 3 press to delete the 3 and then type 7 On the other hand if 34 should have been 384 move the cursor until it is between the 3 and the 4 and then type 8 If the 34 should have been 3 only move the cursor to the right of the 4 and press to delete the 4 Fir
20. to a window with the graph of y x gt 4x Figure IV 18 While the TI 89 is calculating coordinates for a plot it displays the word BUSY on the status line IV 8 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator Technology Tip If you would like to see a function in the Y menu and its graph in a graph window both at the same time press MODE to open the MODE menu and press F2 to go to the second page The cursor will be next to Split Screen Select either TOP BOTTOM or LEFT RIGHT by pressing J and 2 or 3 respectively Now the 2 lines below the Split 1 App line have become readable because these options apply only when the calculator is in the split screen mode The Split 1 App will automatically be the screen you were on prior to pressing MODE You can choose what you want the top or left hand screen to show by moving down to the Split 1 App line pressing J and the number of the application you want in that window The Split 2 App determines what is shown in the bottom or right hand window Press ENTER to confirm your choices and your TI 89 s screen will now be divided either horizontally or vertically as you choose Figure IV 16 show the graph and the Y screen with the settings shown in Figure IV 17 The split screen is also useful when you need to do some calculations as you trace along a graph In split screen mode one side of the screen will be more heavily outlined This is the active scree
21. z0 FS94 36842 HMax 240 S947 46842 20 8 20 8 RAD AFFERO FURL 10 Figure IV 20 Square WINDOW Figure IV 21 Graph of y x 4x RAD AFFERO FUNC To initialize the viewing window quickly to the standard viewing window Figure IV 19 press F2 Zoom 6 ZoomStd To set the viewing window quickly to a square window Figure IV 20 press F2 5 ZoomSqr More information about square windows is presented later in Section IV 2 4 IV 10 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator 10 Fiz F F4 Fr Taos Trace Reararh Fen RAD AFF RON FUNC 10 Figure IV 22 Custom WINDOW Figure IV 23 Graph of y x 4x RAD AFFRON FUNC Sometimes you may wish to display grid points corresponding to tick marks on the axes This and other graph format options may be changed while you are viewing the graph by pressing F1 to get the Tools menu Figure IV 24 and then pressing 9 Format to display the Format menu Figure IV 25 or by pressing KA as indicated on the Tools menu in Figure IV 24 Move the blinking cursor to Grid press 2 ON ENTER to redraw the graph Figure IV 26 shows the same graph as in Figure IV 23 but with the grid turned on Coordindkes RECT GFIFH OFder SEOs Leadinag Cursor OFF Labels Enter gt AVve E gt C CAMCEL RAD AFFRON FUNC Figure IV 26 Grid turned on for y x 4x In general you ll want the grid turned off so do that now by pressi
22. zoom and trace to approximate these extreme values IV 18 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator First trace along the curve near the relative minimum Notice by how much the x values and y values change as you move from point to point Trace along the curve until the y coordinate is as small as you can get it so that you are as close as possible to the relative minimum and zoom in press F2 2 ENTER or use a zoom box Now trace again along the curve and as you move from point to point see that the coordinates change by smaller amounts than before Keep zooming and tracing until you find the coordinates of the relative minimum point as accurately as you need them approximately 1 15 3 08 Follow a similar procedure to find the relative maximum Trace along the curve until the y coordinate is as great as you can get it so that you are as close as possible to the relative maximum and zoom in The relative maximum point on the graph of y x 4x is approximately 1 15 3 08 The TI 89 can automatically find the relative maximum and relative minimum points While viewing the graph press F5 to display the Math menu Figure IV 50 Choose 3 Minimum to calculate the minimum value of the function and 4 Maximum for the maximum You will be prompted to trace the cursor along the graph first to a point left of the minimum maximum press ENTER to set this lower bound Note the arrow nea
23. Editing expressions Then to find the balance from the same initial investment but after 5 years when the annual interest rate is 7 5 press the following keys to change the last calculation above 52 CC Cl me 7 ENTER You could also use the CLEAR key to erase everything to the right of the current location of the cursor Then changing the calculation from 10 years at the annual interest rate of 8 5 to 5 years at the annual interest rate of 7 5 is then done by pressing J J CLEAR 5 KK E m 7 ENTER IV 1 3 Key Functions Most keys on the TI 89 offer access to more than one function just as the keys on a computer keyboard can produce more than one letter g and G or even quite different characters 5 and The primary function of a key is indicated on the key itself and you access that function by a simple press on the key To access the second function indicated in yellow or to the left above a key first press 2nd 2nd appears on the status line and then press the key For example to calculate 25 press 2nd V 25 ENTER Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 3 Technology Tip The TI 89 automatically places a left parenthesis after many functions and operators including 2nd LN K3 e 2nd SIN 2nd COS 2nd TAN and 2nd V If a right parenthesis is not entered the TI 89 will respond with an error message indicating that the right parenth
24. FN and Kd directions Technology Tip Trace along the graph of y 25x and press and hold either the 4 or gt direction The cursor becomes larger and pulses as it moves along the graph Eventually you will reach the left or right edge of the window Keep pressing the direction and the TI 89 will allow you to continue to trace by panning the viewing window Check the WINDOW screen to see that the xmin and xmax are automatically updated If you trace along the graph of y x gt 4x the cursor will eventually move above or below the viewing window The cursor s coordinates on the graph will still be displayed though the cursor itself can no longer be seen When you are tracing along a graph press ENTER and the window will quickly pan over so that the cursor s position on the function is centered in a new viewing window This feature is especially helpful when you trace near or beyond the edge of the current viewing window The TI 89 s display has 159 horizontal columns of pixels and 99 vertical rows So when you trace a curve across a graph window you are actually moving from xmin to xmax in 158 equal jumps each called Ax You xmax xmin 158 friendly numbers like 0 1 or 0 25 so that when you trace along the curve the x coordinates will be incremented by such a convenient amount Just set your viewing window for a particular increment Ax by making xmax xmin 158 Ax For example if you want xmin 5 and Ax 0 3 set xmax
25. IV 3 function graphs main folder floating decimals with 10 digits displayed radian measure normal exponential format real numbers rectangular vectors pretty print full screen display home screen showing approximate calculation mode decimal base international system of units metric measurement and English Note that some of the lines on page 2 and page 3 of the MODE menu are not readable These lines pertain to options that are not set as above Details on alternative options will be given later in this guide For now leave the MODE menu by pressing HOME or 2nd QUIT Some of the current settings are shown on the status line of the home screen PEE Fi Fe F3 Fade L Fa3 c Faae gt POET Fi Fe F3 Fade 1 Fade tifa gt FUNCTION CUFFGnE Folder mgin Diselay Digits FLOAT i Selit Fcreen Sei i FF TSE D gb ae TENargin S Binefar AS DIALS OoJ Anale RADIA Exronential Formak MORMAL Come lex Format REAL vector Format RECTAMGULAR Fretky Print DH Enter 2Ave E C CAMCEL UE AND TO OFEN CHOICE Figure IV 1 MODE menu page 1 Tir rA o oe Exac APPROX PEE Fi Fe F3 Fade iPade z Fade 3 a Unit eskem hat LITS Language E Enter FAVE ESC CANCEL USE AND TO OFEN CHOICES Figure IV 3 MODE menu page 3 Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 1 IV 1 2 Editing One advantage of the TI 89 is that you can use
26. N 1 4 ENTER 7 ENTER Figure IV 93 Press 2nd QUIT to return to the home screen To find the 18th term of this sequence calculate u1 18 by pressing alpha U 1 18 ENTER see Figure IV 94 Fir F3 F4 F r Fr Fir Fer For For Tools Edit SEV Te AzeGS Too Ts AIs amp br acae Clean Ue FLOT i ich lite RAD APFROR SEQ RAD AFFROH SEQ Figure IV 93 Sequence Y menu Figure IV 94 Sequence mode Of course you could also use the explicit formula for the nth term of an arithmetic sequence t a n 1 d First enter values for the variables a d and n then evaluate the formula by pressing aloha A alpha N 1 aloha D ENTER For a geometric sequence whose nth term is given by t a r enter values for the variables a n and r then evaluate the formula by pressing alpha A alpha R alpha N 1 ENTER To use the explicit formula in sequence mode make u1 7 n 1 4 by pressing KJ Y then using PN to move up to the u1 line and pressing CLEAR 7 N 1 x 4 ENTER 2nd QUIT Once more calculate u1 18 by pressing aloha U 1 18 ENTER Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 33 IV 7 4 Finding Sums and Partial Sums of Sequences You can find the sum of a sequence by combining the sum feature with the seq feature on the List sub menu of the MATH menu The format of the sum command is SuM list The format of the seq command is Seq ex
27. Part IV Texas Instruments TI 89 IV 1 Getting started with the TI 89 In this guide the key with the green diamond symbol inside a green border will be indicated by El the key with the white arrow pointing up inside a white border the shift key will be indicated by Hi and the key with the white arrow the backspace key pointing to the left will be indicated by ES There are 5 blue keys below the calculator screen labeled F1 through F5 These function keys have different effects depending on the screen that is currently showing The effect or menu of the function keys corresponding to a screen are shown across the top of the display IV 1 1 Basics Press the ON key to begin using your TI 89 If you need to adjust the display contrast first press and hold Ei then press the minus key to lighten or the plus key to darken When you have finished with the calculator turn it off to conserve battery power by pressing 2nd and then OFF Check our TI 89 s settings by pressing MODE If necessary use the arrow keys to move the blinking cursor to a setting you want to change You can also use F1 to go to page 1 F2 to go to page 2 and F3 to go to page 3 of the MODE menu To change a setting use Kd to get to the setting that you want to change then press gt to see the options available Use PN or Kd to highlight the setting you want and press ENTER to select the setting To start with select the options shown in Figures IV 1 IV 2 and
28. V 88 Reduced row echelon form 1 2 3 IV 6 4 Determinants and Inverses Enter this 3 x 3 matrix as a 1 3 0 Because this consists 2 5 5 of the first three columns of the matrix a that was previously used you can go to the matrix move the cursor into the fourth column and press 2nd F6 Util 2 Delete 3 column This will delete the column 2 3 that the cursor is in To calculate its determinant 1 3 0 go to the home screen and press 2nd 2 o 5 MATH 4 2 det aloha A ENTER You should find that the determinant is 2 as shown in Figure IV 89 Fir Fer For For Too sal ebraycate Clean Ur E deta Aa feo 2a 4 5 Sed aa 1 3 io wa FAD APPROS FUNC Figure IV 89 a and a Because the determinant of the matrix is not zero it has an inverse matrix Press alpha A 1 ENTER to calculate the inverse of matrix a The result is shown in Figure IV 89 Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 31 Now let s solve a system of linear equations by matrix inversion Once again consider x 2y 3z 9 I 3 y Oy 4 The coefficient matrix for this system is the matrix 1 3 O which was 2x Sy 5z 17 2 i 5 9 entered as a in the previous example Now enter the 3 x 1 matrix 4 as b Because b was used before 17 when we stored 2a as b press APPS 6 2 Open J 2 Matrix KA Ka J and use Kd to move the cursor to b then pre
29. aph that extends horizontally from 10 to 10 and vertically from 10 to 10 Press KA WINDOW to see information about your viewing window Figure IV 19 shows the WINDOW screen that corresponds to the viewing window in Figure IV 18 This is the standard viewing window for the TI 89 Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 9 The variables xmin and xmax are the minimum and maximum x values of the viewing window ymin and ymax are the minimum and maximum y values xscl and yscl set the spacing between the tick marks on the axes xres sets pixel resolution 1 through 10 for function graphs FAD AFFRON FUNC Figure IV 19 Standard WINDOW Technology Tip Small xres values improve graph resolution but may cause the TI 89 to draw graphs more slowly Use PN and Kd to move up and down from one line to another in this list pressing the ENTER key will move down the list Press CLEAR to delete the current value and then enter a new value You may also edit the entry as you would edit an expression Remember that a minimum must be less than the corresponding maximum or the TI 89 will issue an error message Also remember to use the key not which is subtraction when you want to enter a negative value Figures V 18 19 IV 20 21 and IV 22 23 show different WINDOW screens and the corresponding viewing window for each one 10 rhetlebam reoie zeom trace nesrorn tiath erac Pen smin
30. e deletion from the calculator s memory Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 39 Technology Tip If your program uses one letter variables such as a b C or d note that any previous values for these variables including matrices will be replaced by the values used by the program The TI 89 does not distinguish between A and a in these uses Note that you will have to clear the variables using 2nd VAR LINK in order to use these names again in the current folder From the home screen press F4 Other aloha B NewFold and type the name of the new folder The work you do from that point on will be in the new folder as indicated by the folder name in the lower left corner of the status line You can change folders from the MODE menu or from the home screen by typing setFold foldername where foldername is the existing folder that you wish to be in IV 10 2 Executing a Program To execute a program you entered go to the home screen and type the name of the program including the parentheses and then press ENTER to execute it If you have forgotten its name press 2nd VAR LINK to list all the variables that exist The programs will have PRGM after the name You can execute the program from this screen by highlighting the name and then pressing ENTER The screen will return to the home screen and you will have to enter the closing parenthesis and press ENTER to execute the program If you
31. es by pressing ZN or Ad IV 10 Programming IV 10 1 Entering a Program The TI 89 is a programmable calculator that can store sequences of commands for later replay Press APPS 7 Program Editor to access the programming menu The TI 89 has space for many programs each called by a title you give it To create a new program start by pressing APPS 7 3 New Set the Type to Program and the Folder to main unless you have another folder in which you want to store the program Enter a descriptive title for the program in the Variable line After you name the program press ENTER ENTER to go to the program editor The program name and the beginning and ending commands of the program are automatically displayed with the cursor on the first line after Prgm the begin program command In the program each line begins with a colon supplied automatically by the calculator Any command you could enter directly in the TI 89 s home screen can be entered as a line in a program There are also special programming commands You may interrupt programming input at any stage by pressing 2nd QUIT To return later for more editing press APPS 7 2 Open move the cursor down to the Variable list highlight the program s name and press ENTER ENTER You may remove a program from memory by pressing 2nd VAR LINK move the cursor to highlight the name of the program you want to delete then press F1 Manage 1 Delete ENTER and then ENTER again to confirm th
32. esis 1s missing When you want to use a function printed in green or to the right above a key first press Kl appears on the status line and then press the key For example if you are in exact calculation mode and want to find the approximate value of 45 press 2nd V 45 Kal The TI 89 can produce both upper and lower case letters When you want to use a lower case letter printed in purple or to the right above a key first press alpha a lower case a appears on the status line and press the key For example to use the letter k in a formula press aloha K If you need several letters in a row press 2nd a lock and then press all the letters you want Remember to press aloha when you are finished and want to restore the keys to their primary functions To type upper case letters press and then press the letter To lock in upper case letters press alpha an upper case A appears on the status line To restore the keys to their primary functions press alpha Technology Tip There are separate keys for the commonly used letters X Y Z and T A simple press of the key will produce a lower case letter while pressing and then the key will produce an upper case letter IV 1 4 Order of Operations The TI 89 performs calculations according to the standard algebraic rules Working outwards from inner parentheses calculations are performed from left to right Powers and roots are evaluated first followed by multiplications and d
33. ghton Mifflin Company All rights reserved IV 19 10 Fiz F F4 Fr Taos Trdce Reararh Fen 10 RAD AFF RON FURL 10 Figure IV 54 Graph of y x 1 Fir Fer For For Tao Ts All ebrapla de Clean Ur Drawlnue x 34 1 HAIN RAD AFFRON FUNC Figure IV 56 Drawlnv Fir F3 F4 For ii Taos Trace Reararh Dr dk Gta 1 ClrOraw JE Craw arn UrawSlp Tafa r T g COA RTT ERE Lepri gpu Tangu I on eee on 4s Je Di eS m soa TYFE OF UZE T CEMTER OF CESC Figure IV 55 Draw menu 10 Fir F3 F4 Fr Taos Trace Reararh Fen RAD AFFERO FUNC 10 Figure IV 57 Graph of y x 1 and its inverse function IV 2 10 Tangent Lines Once again graph y x 1 in the standard viewing window see Figure I V 54 The TI 89 can draw the tangent line to a graph of a function at a specified point Press F5 alpha A Tangent You are prompted to enter a value for x So press or J to select a point or enter a value for x see Figure IV 58 Press 1 ENTER The graph of the original function and the tangent line to the graph at x 1 will be displayed see Figure I V 59 Note that the equation of the tangent line is displayed at the bottom of the screen To clear the tangent line press 2nd F6 1 10 Fir F3 F4 Fr Taos Trdce Reararh Fen 1 10 Tangent at wor 126552205 yor 1 00202572 TYFE OF USE CENTER OF LESC 10 Figure IV 58 Tangent IV 20 Copyright
34. her way to display the terms of a sequence is to enter the sequence and the number of terms you want listed For example to find the first five terms of the sequence u n 4 press 2nd MATH 3 List 1 seq aloha N 4 alphaN 1 5 1 ENTER see Figure IV 92 The format of this command is Seq expression variable low high step Fir Fer For For Too sal ebraycatec Clean Ur E zegi n 4 n 1 5 1 Di ae 1 HARIH RAD AFFERO FUNC Figure IV 92 Terms of sequence u n 4 IV 7 3 Arithmetic and Geometric Sequences Use iteration with the ANS variable to determine the nth term of a sequence For example find the 18th term of an arithmetic sequence whose first term is 7 and whose common difference is 4 Enter the first term 7 then start the progression with the recursion formula 2nd ANS 4 ENTER This yields the 2nd term so press ENTER sixteen more times to find the 18th term 75 For a geometric sequence whose common ratio is 4 start the progression with 2nd ANS x 4 ENTER You can also define the sequence recursively with the TI 89 by selecting SEQUENCE in the Graph type on the first page of the MODE menu see Figure IV 1 Once again let s find the 18th term of an arithmetic sequence whose first term is 7 and whose common difference is 4 Press MODE J 4 SEQUENCE ENTER Then press KJ Y to edit any of the TI 89 s sequences U1 through u99 Make u1 ul n 1 4 and uil 7 by pressing aloha U 1 alpha
35. igure IV 102 Polar Y menu Figure IV 103 Polar graph of r 4 sin 0 IV 9 Probability and Statistics IV 9 1 Random Numbers The command rand generates numbers You will find this command in the Probability sub menu of the MATH menu Press 2nd MATH 7 4 rand ENTER to generate a random number between 0 and 1 Press ENTER to generate another number keep pressing ENTER to generate more of them If you need a random number between say 0 and 10 then press 10 2nd MATH 7 4 ENTER To get a random number between 5 and 15 press 5 10 2nd MATH 7 4 ENTER IV 36 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator If you need the random number to be an integer between 1 and 10 inclusive press 2nd MATH 7 4 10 ENTER For a random negative integer between 1 and 10 inclusive press 2nd MATH 7 4 10 ENTER IV 9 2 Permutations and Combinations To calculate the number of permutations of 12 objects taken 7 at atime P press 2nd MATH 7 2 nPr 12 7 ENTER So P 3 991 680 as shown in Figure IV 104 Fir Fer Fo For Too sal tbra Cale Clean Ur erPeole 73 399316850 Brilroie 7 roe HARIH RAD AFFERO FOL r E Figure IV 104 P and C For the number of combinations of 12 objects taken 7 at a time C press 2nd MATH 7 3 nCr 12 7 ENTER So C 792 as shown in Figure IV 104 IV 9 3 Probability of Winning A state lottery is configured so that each p
36. ivisions and then additions and subtractions Note that the TI 89 distinguishes between subtraction and the negative sign If you wish to enter a negative number it is necessary to use the key For example you would calculate 5 4 3 by pressing 5 4 x 3 ENTER to get 7 Enter these expressions to practice using your TI 89 Expression Keystrokes Display i faa tars 7 5 x 3 ENTER 8 TEE Gone 7 5 x 3 ENTER 6 120 10 120 10 2 ENTER 20 120 10 120 10 2ENTER 12100 s 24 2 3 ENTER 3 24 2 24 2 3 ENTER 1728 7 5 3 7 5 x 3 ENTER 36 l l N N 1 IV 1 5 Algebraic Expressions and Memory Your calculator can evaluate expressions such as a after you have entered a value for N Suppose you want N 200 Press 200 STO gt alpha N ENTER to store the value 200 in memory location N Whenever you use N in an expression the calculator will substitute the value 200 until you make a change by storing another number in N Next enter the expression NWN 1 Mw by typing alpha N x aloha N 1 2 ENTER For N 200 you find that NN 1 ees ar a 20 100 Note that there is no distinction made between upper and lower case letters in this case The contents of any memory location may be revealed by typing just its letter name and then ENTER And the TI 89 retains memorized values even when it is turned off so long as its batteries are good IV 4 Copy
37. layer chooses six different numbers from 1 to 40 If these six numbers match the six numbers drawn by the State Lottery Commission the player wins the top prize There are 49C ways for the six numbers to be drawn If you purchase a single lottery ticket your probability of winning is 1 in C Press 1 2nd MATH 7 3 40 6 ENTER to calculate your chances but don t be disappointed IV 9 4 Sum of Data The following data are a student s scores on 8 quizzes and 2 tests throughout an algebra course 25 20 18 89 17 24 23 22 25 93 To find the total points earned by the student first enter the data using the TI 89 s list editor Press APPS 6 3 3 List KA KA C O R E S ENTER ENTER to open a new variable called SCORES see Figure IV 105 Now begin entering the test scores as shown in Figure IV 106 Then press 2nd QUIT To find the sum of the scores press 2nd MATH 3 6 2nd a lock S C O R E S alpha ENTER From Figure IV 107 the student earned 356 points throughout the algebra course Tipe e e A Tom Ts F IGE Schur Ce Header Eak ae ee o on Folder VOR rob Te Rape attr diese faidnaciive E ESC CANCEL TYFE CEMTERI EOK AMD CESCI CAMCEL RAD AFF RON FOL Figure IV 105 Entering a new variable Figure IV 106 List editor Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved TV 37 Fir Fer Fo For Too Ts Al ebra pla de Clean UF E SUM Scores SUMC Scores RAD AFFERO FOL
38. mathematical operations Try them for practice on your TI 89 Expression Keystrokes Display 3 2 42 2nd V 3 2 4 2 ENTER 5 2 2 3 1 ENTER 2 333333333 In 200 2nd LN 200 ENTER 5 298317367 2 34 10 2 34 x 10 5 ENTER 234000 Technology Tip Note that if you had set the calculation mode to either AUTO or EXACT page 2 of the MODE menu the TI 89 would display f for 25 and In 200 for In 200 So you can use either fractions and exact numbers or decimal approximations The AUTO mode will give exact rational results whenever all of the numbers entered are rational and decimal approximations for other results Additional mathematical operations and functions are available from the MATH menu Press 2nd MATH to see the various sub menus Figure IV 8 Press 1 Number or just ENTER to see the options available under the Number sub menu Figure IV 9 You will learn in your mathematics textbook how to apply many of them As an example calculate the remainder of 437 when divided by 49 by pressing 2nd MATH 1 Number then either aloha A remain or K4 Ka hd Bd hd Bd hd Bd AA ENTER finally press 437 49 ENTER to see 45 To leave the MATH menu or any other menu and take no other action press 2nd QUIT or just ESC Note that you can select a function or a sub menu from the current menu by pressing either B4 until the desired item is highlighted and then ENTER or by pressing the number or letter corresponding to the function or sub menu It is ea
39. move your cursor closer to get the best approximation possible for the coordinates of the intersection Fir F3 F4 Fr Taos Trace Reararh Fen OHOG2YS6962 yoi 7 463155 HAIN RAD AFFRON FUNC 2 5 Figure IV 41 New WINDOW Figure IV 42 Closer view RAD AFF RON FUNC A more efficient method for enlarging the view is to draw a new viewing window with the cursor Start again with a graph of the two functions y x 4x and y 25x in a standard viewing window press F2 6 for the standard viewing window Now imagine a small rectangular box around the intersection point near x 2 Press F2 1 ZoomBox Figure IV 43 to draw a box to define this new viewing window Use the arrow keys to move the cursor whose coordinates are displayed at the bottom of the window to one corner of the new viewing window you imagine Press ENTER to fix the corner where you moved the cursor it changes shape and becomes a blinking square Figure IV 44 Use the arrow keys again to move the cursor to the diagonally opposite corner of the new window Figure IV 45 Note that you can press and hold ZN or Ad with lt 4 or gt for this If this box looks all right to you press ENTER The rectangular area you have enclosed will now enlarge to fill the graph window Figure IV 46 IV 16 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator 10 Fir F3 F4 Fr Taos Trdce Reagrarh Fen Fir Brae Fe F4 Taos nto Trace Re aro
40. n 1 e the screen that you can currently modify You can change which side is active by using 2nd to access the symbol above the APPS key For now restore the TI 89 to Full screen Technology Tip Note that if you set one part of your screen to contain a table and the other to contain a graph the table will not necessarily correspond to the graph unless you use KA TblSet to generate a new table based on the functions being graphed as in Section IV 2 1 Fir ER F7 A Tools Trace Reararh Fen Fi Fe F Fade Fae c PFade a Sei fcrecn LEFT RIGHT Teli i AFF Gor TFT AFF Y Editor Humber OF GFOERS 1 DIJEL Ll n ao DMB IENS e m C te TEOR ied _ EXack APROX Ew _ CEnberSeAve ESC CHMCEL RAO AFFROW FUNC UZE AHO TO OFEN CHOICES Figure IV 16 Split screen LEFT RIGHT Figure IV 17 MODE settings for Figure IV 16 AFFROSIMATE DEC gt Your graph window may look like the one in Figure IV 18 or it may be different Because the graph of y xX 4x extends infinitely far left and right and also infinitely far up and down the TI 89 can display only a piece of the actual graph This displayed rectangular part is called a viewing window You can easily change the viewing window to enhance your investigation of a graph 10 Fir F F4 Fr Taos Trace Reararh Fen RAD AFFRON FUNC 10 Figure IV 18 Graph of y x 4x The viewing window in Figure IV 18 shows the part of the gr
41. n graphs the cursor will not move to values outside of the t range so 4 will not work when t 0 and gt will not work when t 27 As you trace along this graph notice that the cursor moves in the counterclockwise direction as t increases IV 8 2 Rectangular Polar Coordinate Conversion The Angle sub menu of the MATH menu provides a function for converting between rectangular and polar coordinate systems These functions use the current angle measure setting so it is a good idea to check the default angle measure before any conversion Of course you may override the current angle measure setting as explained in Section IV 4 1 For the following examples the TI 89 is set to radian mode Given the rectangular coordinates x y 4 3 convert from these rectangular coordinates to polar coordinates r 0 by pressing 2nd MATH 2 5 R gt Pr 4 3 ENTER to display the value of r Now press 2nd MATH 2 6 R P6 4 3 ENTER to display the value of 6 see Figure TV 100 Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 35 Fir Fer F For Fir Fer Fir For Too MAlebrapCate Clean UF Too AlebeapCaiec Clean UF BRRPrO4 73 BPRRxC3 1 EKPA 4 73 7 643501 1085 ePRRYCS T HAIN RAD APFRON PAR FEN HAIN RAD APFRON FAR Figure IV 100 Rectangular to polar coordinates Figure IV 101 Polar to rectangular coordinates Suppose r 0 3 7 To convert from these polar coordinates to
42. ng KA and turning the Grid option to OFF then pressing ENTER IV 2 3 Graphing Step and Piecewise Defined Functions The greatest integer function written x gives the greatest integer less than or equal to a number x On the TI 89 the greatest integer function is called floor and is located under the Number sub menu of the MATH menu Figures IV 8 9 So calculate 6 78 6 by pressing 2nd MATH 1 6 floor 6 78 ENTER To graph y x go into the Y menu move beside y1 and press CLEAR 2nd MATH 16 X ENTER K3 GRAPH Figure IV 27 show this graph in a viewing window from 5 to 5 in both directions Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 11 The true graph of the greatest integer function is a step graph like the one in Figure IV 28 For the graph of y x a segment should not be drawn between every pair of successive points You can change this graph from a Line to a Dot graph on the TI 89 by going to the Y screen moving the cursor up until this function is selected highlighted and then pressing 2nd F6 Style This opens the Graph Style menu Move the cursor down to the second line and press ENTER or press 2 to have the selected graph plotted in Dot style Now press K GRAPH to see the result 3 2 Fir F3 F4 Fr Fir F3 F4 Fr Taos Trace Reararh Fen Taos Trdce Reararh Fen RAD AFFERO FUNC RAD AFFERO FUNE 5 o Figure IV 27 Line graph of y x Figure IV 28 Dot gra
43. ngle equation 2x 5 2x 1 which simplifies to 4x 4 0 So you may also graph y 4x 4 and find its x intercept to solve the system or use the solve function 3 oe IV 3 4 Solving Inequalities by Graphing Consider the inequality 1 gt x 4 To solve it with your 3 l l TI 89 graph the two functions y 1 and y x 4 Figure IV 68 First locate their point of l l a IN es intersection at x 2 The inequality is true when the graph of y 1 gt lies above the graph of y x 4 and that occurs when x lt 2 So the solution is x lt 2 or o0 2 10 Fir F3 F4 Fr Taos Trdce Reararh Fen 10 Intersection MOG RAD AFFRON FUNC 10 3 Figure IV 68 Solving 1 gt x 4 The TI 89 is capable of shading the region above or below a graph or between two graphs For example to graph y gt x 1 first enter the function y x 1 as y1 Then highlight y1 and press 2nd F6 7 Above see Figure IV 69 These keystrokes instruct the TI 89 to shade the region above y x 1 Press K3 GRAPH to see the graph The region above the graph will be shaded using the default shading option of vertical lines as in Figure IV 70 Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 23 Fir F3 F4 Fr Tools Trace Reararh Fen Iry 2 HAIN RAD AFFROR FUNC RAD AFFRON FUNC 10 Figure IV 69 Shade Above style Figure IV 70 G
44. not just the character or value to the left of the cursor So move the cursor to any value you wish to change then type the correction To insert or delete a data point move the cursor over the data point cell you wish to add or delete To insert a cell move to the cell below the place where you want to insert the new cell and press 2nd F6 Util 1 Insert 1 cell and a new empty cell is open IV 5 2 Plotting Data First check the MODE screen Figure IV 1 to make sure that you are in FUNCTION graphing mode With the data points showing press F2 Plot Setup to display the Plot Setup screen If no other plots have been entered Plot 1 is highlighted by default Press F1 Define to select the options for the plot Use PN K4 and ENTER to select the Plot Type as Scatter and the Mark as a Box Press alpha C 1 to set the independent variable x and press alpha C 2 to set the dependent variable y as shown in Figure IV 75 then press ENTER to save the options and press KA GRAPH to graph the data points Make sure that you have cleared or turned off any functions in the Y screen or those functions will be graphed simultaneously Figure V 76 shows this plot in a window from 0 to 15 horizontally and vertically You may now press F3 Trace to move from data point to data point aa calien TaolsZoom Trace Reararh ii Pot Pi Scatter Box TRB A ae ee ee Dd ible grabeno Enter ZAVE ESC CAMCEL RAD AFERON FUNC RAD ARPROR FUNC Figure IV
45. ored in e and replaces the previous matrix e The last step of the row operations is shown in Figure IV 86 Row Operation Keystrokes Add row to row 2 2nd MATH 4 alpha J 2 alpha E 1 2 STO gt aloha E ENTER Add 2 times row 1 to row 3 2nd MATH 4 alpha J 4 2 alpha E 1 3 STO gt aloha E ENTER Add row 2 to row 3 2nd MATH 4 alpha J 2 alpha E 2 3 STO gt alpha E ENTER Multiply row 3 by 5 2nd MATH 4 alpha J3 1 2 alpha E 3 STOP aloha E ENTER Figure IV 86 Row echelon form of matrix after row operations So z 2 y l andx 1 IV 30 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator Technology Tip The TI 89 can produce a row echelon form and the reduced row echelon form of a matrix The row echelon form of matrix a is obtained by pressing 2nd MATH 4 3 ref alpha A ENTER see Figure IV 87 and the reduced row echelon form is obtained by pressing 2nd MATH 4 4 rref alpha A ENTER see Figure IV 88 Note that the row echelon form of a matrix is not unique so your calculator may not get exactly the same matrix as you do by using row operations However the matrix that the TI 89 produces will result in the same solution to the system Fir Fer Fo For Fir Fer For For Tao Ts Alebr ala de Clean Ur Taos Al ebrapCa de Clean Ur Bre a feo Lao ao l Da J D G l RAD APFRON FUNC RAD APFRON FUNC EEN Figure IV 87 Row echelon form Figure I
46. ormat This cursor is called a free moving cursor because it can move from dot to dot anywhere in the graph window Remove the free moving cursor and its coordinates from the window by pressing KA GRAPH CLEAR ESC or ENTER Press the cursor directions again and the free moving cursor will reappear at the same point you left it 10 Fir F3 F4 Fr Tools Trdce Reararh Fen 10 moe TL G12658 uci g 2105263 RAD AFPRON FUNC 10 Figure IV 35 Free moving cursor Press F3 Trace to enable the left 4 and right gt directions to move the cursor from point to point along the graph of the function The cursor is no longer free moving but is now constrained to the function The coordinates that are displayed belong to points on the function s graph so the y coordinate is the calculated value of the function at the corresponding x coordinate Figure IV 36 10 Fir F3 F4 Fr Taos Trace Reararh Fen 1 10 moe 724050635 uci g 214252 RAD AFFRON FUNC 10 Figure IV 36 Trace RAD AFFERO FUNC RAD AFFERO FUNC 10 Figure IV 37 Two functions Figure IV 38 y x 4x and y 25x IV 14 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator Now plot a second function y 25x along with y x 4x Press Kl Y and enter 25x for y2 then press KA GRAPH to see both functions Notice that in Figure IV 37 there are checkmarks Vv to the left of both y1 and y2
47. page of the MODE menu where angle measure is selected Then press gt to display the options Use FN or A4 to move from one option to the other Either press the number corresponding to the measure or when the measure is highlighted press ENTER to select it Then press ENTER to confirm your selection and leave the MODE menu IV 24 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator It s a good idea to check the angle measure setting before executing a calculation that depends on a particu lar measure You may change a mode setting at any time and not interfere with pending calculations From the home screen try the following keystrokes to see this in actions Expression Keystrokes Display sin 45 MODE BA bA Bd J kA ENTER ENTER 2nd SIN 45 ENTER 7071067812 sin 77 2nd SIN 2nd 7 ENTER 0548036651 sin 77 MODE Bd BA bA J PS ENTER ENTER 2nd SIN 2nd 7 ENTER 0 sin 45 2nd SIN 45 ENTER 8509035245 sin 2nd SIN 2nd 7 6 ENTER 5 The first line of keystrokes sets the TI 89 in degree mode and calculates the sine of 45 degrees While the calculator is still in degree mode the second line of keystrokes calculates the sine of m degrees approximately 3 1415 The third line changes to radian mode just before calculating the sine of 7 radians The fourth line calculates the sine of 45 radians Finally the fifth line calculates the sine of radians the calculator remains in radian mode The TI 89 make
48. ph of y fx Technology Tip When graphing functions in the Dot style it improves the appearance of the graph to set xres to 1 Figure IV 28 was graphed with xres 1 Also the default graph style is Line so you have to set the style to Dot each time you wish to graph a function in Dot mode The TI 89 can graph piecewise defined functions by using the when function The when function is not on any of the keys but can be found in the CATALOG or typed from the keys The format of the when function is when condition trueResult falseResult unknownResult where the falseResult and unknownResult are optional arguments 2 x i g 7 o using Dot graph you want to graph x 2 when the condition x lt 0 is true and graph x 1 when the condition is false First clear any existing functions in the Y screen Then move to the y1 line and press 2nd a lock W H E N alpha X 2nd lt 0 X 2 2 X 1 ENTER Figure IV 29 Then press KA GRAPH to display the graph Figure IV 30 shows this graph in a viewing window from 5 to 5 in both directions This was done in Dot style because the TI 89 will incorrectly connect the two sides of the graph at x O if the function is graphed in Line style For example to graph the function f x 5 Fir F F4 Fr Taos Trace Reararh Fen M LEE aaa H1txs whent s i xtA 1i HAIN RAD AFFRON FUNC RAD AFFROR FUNC 5 Figure IV 29 Piecewise defined function Figure IV 30 Piecewise defined graph O
49. pression variable low high step where the step argument is optional and the default is for integer values from low to high 12 For example suppose you want to find the sum gt 4 0 3 Press 2nd MATH 3 6 sum 2nd MATH 3 1 4 n 1 3 alpohaN alphaN 1 12 ENTER Figure IV 95 The seq command generates a list which the Sum command then sums Note that any letter can be used for the variable in the sum i e the N could just have easily been an A or a K Fir Fer Fo For Too sal ebraycate Clean Ur m sum seal 4 3 ial iz 1 14784803 SsuMmCseqcdao SI AN A d 1219 RAD AFFERO SEQ 12 Figure IV 95 4 0 3 n 1 Now calculate the sum starting at n O by using gt i and to edit the range You should obtain a sum of approximately 5 71284803 The seq feature can also be combined with the cumSum feature to find partial sums of a series The IV 33 format of the cumSum command is cumSum iis 4 For example suppose you want to find the first four partial sums of the series gt 3 1 Press 2nd MATH n l 3 7 cumSum 2nd MATH 3 1 3 alpha N 1 alpha N 1 4 ENTER Figure IV 96 Fir Fer F F For Tootsil tbra Cale Clean UF scumsumlseql S771 ALi all SE a iir SEE SUM segia intin d 420 RAD AFFRON SEG 4 Figure IV 96 Partial sums of antl n 1 IV 8 Parametric and Polar Graphs IV 8 1 Graphing Parametric Equations The T1 89 plots up to 99 pairs of parametric equations
50. pt of a function s graph is a zero of the function so while viewing the graph press F5 Figure IV 50 and choose 2 Zero to find a zero of this function Set a lower bound and upper bound as described in Section V 2 8 The TI 89 shows the coordinates of the point and indicates that it is a zero Figure IV 62 10 Fiz F F4 Fr Taos Trace Reararh Fen Woe RAD AFFERO FURL 10 Figure IV 62 A zero of y x 8x Trace and Zoom are especially important for locating the intersection points of two graphs say the graphs of y x gt 4x and y 25x Trace along one of the graphs until you arrive close to an intersection point Then press FN or B4 to jump to the other graph Notice that the x coordinate does not change but the y coordinate is likely to be different Figures IV 63 and IV 64 Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 21 10 10 Fir F F4 Fr Fir F3 F4 Fr Tools Trace Reararh Fen Taos Trace Reararh Fen 1 2 10 RAG AFF ROK FURL ajo 10 Figure IV 63 Trace on y x gt 4x Figure IV 64 Trace on y 25x RAD AFF RON FURL When the two y coordinates are as close as they can get you have come as close as you now can to the point of intersection So zoom in around the intersection point then trace again until the two y coordinates are as close as possible Continue this process until you have located the point of intersection with as much accu
51. r the top of the display marking the lower bound as in Figure IV 52 Minimum mcr T1 154F 01 F uct 3 0 92701 FAD AFFRON FUNE Upper Bound wor 1 645597 yor TZ 26242 TYFE OF USE CENTER OF LESC 10 Figure IV 52 Finding a minimum Figure IV 53 Relative minimum on y x 4x Now move to a point right of the minimum maximum and set an upper bound by pressing ENTER The coordinates of the relative mintmum maximum point will be displayed see Figure V 53 Good choices for the lower and upper bounds can help the TI 89 work more efficiently and quickly Note that if you have more than one graph on the screen the upper right corner of the TI 89 screen will show the number of the function whose minimum maximum is being calculated IV 2 9 Inverse Functions The TI 89 draws the inverse function of a one to one function Graph y x 1 as y1 in the standard viewing window see Figure IV 54 Next press 2nd F6 Draw to display the Draw menu see Figure IV 55 then press 3 Drawlnv You are automatically returned to the home screen Press X 3 1 ENTER see Figure IV 56 These keystrokes instruct the TI 89 to draw the inverse function of y x 1 The original function and its inverse function will be displayed see Figure IV 57 Note that the calculator must be in function mode in order to use DrawlInv To clear the graph of the inverse function press 2nd F6 1 C rDraw Graphing Technology Guide Copyright by Hou
52. racy as necessary The points of intersection are approximately 2 062 0 515 0 0 and 2 062 0 515 You can also find the point of intersection of two graphs by pressing F5 5 Intersection Trace with the cursor first along one graph near the intersection and press ENTER then trace with the cursor along the other graph and press ENTER Marks are placed on the graphs at these points Then set the lower and upper bounds for the x coordinate of the intersection point and press ENTER again Coordinates of the intersection will be displayed at the bottom of the window More will be said about the Intersection feature in Section IV 3 3 IV 3 2 Solving Equations by Graphing Suppose you need to solve the equation 24x3 36x 17 0 First graph y 24x3 36x 17 in a window large enough to exhibit all its x intercepts corresponding to all the equation s real zeros roots Then use Zoom and Trace or the TI 89 s zero finder to locate each one In fact this equation has just one real solution x 1 414 Remember that when an equation has more than one x intercept it may be necessary to change the viewing window a few times to locate all of them The TI 89 has a solve function To use this function you must be in the home screen To solve the equation 24x 36x 17 0 press 2nd MATH 9 1 solve 24 X 3 36 X 17 0 X ENTER The TI 89 displays the value of the zero Figure IV 65 Note that any letter co
53. raph of y gt x 1 Now use shading to solve the previous inequality 1 gt x 4 The solution is the region which is below 3 l the graph of y 1 and above y x 4 First graph both equations Then from the graph screen press F5 alpha C Shade The TI 89 will prompt for the function that you want to have the shading above Use FN or Kd to move the cursor to the graph of y x 4 then press ENTER The TI 89 will then prompt for the function that you want to have the shading below so use FN or Ad to move the cursor to the graph 3 of y 1 5 and press ENTER The TI 89 will then prompt for the lower bound then the upper bound which are the left and right edges respectively of the extent of the shading If you do not enter a lower or upper bound the values of xmin and xmax will be used So in this case press ENTER twice to set the 3 lower and upper bounds The shaded area extends left from x 2 so the solution to 1 j gt x 4is x lt 2 or o0 2 see Figure IV 71 resis Theile im Resrarh HAIH W a FUNC 10 Figure IV 71 Graph of 1 2 gt x 4 IV 4 Trigonometry IV 4 1 Degrees and Radians The trigonometric functions can be applied to angles measured either in radians or degrees but you should take care that the TI 89 is configured for whichever measure you need Press MODE to see the current settings Press RA three times and move down to the fourth line of the first
54. ress KA TABLE or APPS 5 Table enter 2230 in the x column and press ENTER see Figure IV 15 Press RA to move to the next line and continue to enter additional values for x The TI 89 automatically completes the table with the cor responding values of y1 Press 2nd QUIT to leave the TABLE screen xo fd 2230 2198 1 65 2161 an a ar a FAD AFFROR FUNC TEN RAD AFFROH FUNC Figure IV 14 TABLE SETUP screen Figure IV 15 Table of values Technology Tip The TI 89 requires multiplication to be expressed between variables so xxx does not mean x rather it is a new variable named xxx So you must use either x s between the x s or for powers of x Of course expressed multiplication is not required between a constant and a variable See your TI 89 manual for more information about the allowed usage of implied multiplication IV 2 2 Functions in a Graph Window Once you have entered a function in the Y screen of the TI 89 just press KA GRAPH to see its graph The ability to draw a graph contributes substantially to our ability to solve problems For example here is how to graph y x gt 4x First press Kl Y and delete anything that may be there by moving with the arrow keys to y1 or to any of the other lines and pressing CLEAR wherever necessary Then with the cursor on the now cleared top line y1 press X 3 4 X ENTER to enter the function as in Figure IV 16 Now press KA GRAPH and the TI 89 changes
55. rh 1 Zoo0mBox T St Zoomiut 4 ZoomDec J 2M S4r 40 Di Aoo0mStd recfoomlrig ob oom Trt sng Corner worl 3924051 f uc 1 315759 USE T ENTER OF LESC 10 Figure IV 43 Zoom menu Figure IV 44 One corner selected TYFE OF UZE T CEMTER OF CESC You may cancel the zoom any time before you press this last ENTER Press F2 once more and start over Press ESC or KA GRAPH to cancel the zoom or press 2nd QUIT to cancel the zoom and return to the home screen 0 79 Fir F3 F4 Fr Taos Trace Reararh Fen 10 Fir F3 F4 Fr Taos Trace Reararh Fen 1 39 2 18 10 10 2nd Corner xoi POds1Ol fo uct e947 369 RAD AFFRON FUNC RAD AFFRON FUNC 10 1 32 Figure IV 45 Box drawn Figure IV 46 New viewing window You can also quickly magnify a graph around the cursor s location Return once more to the standard viewing window for the graph of the two functions y x 4x and y 25x Press F2 2 Zoomin and then move the cursor as close as you can to the point of intersection near x 2 see Figure IV 47 Then press ENTER and the calculator draws a magnified graph centered at the cursor s position Figure IV 48 The range variables are changed to reflect this new viewing window Look in the WINDOW menu to verify this 1 97 10 Fir F F4 Fr Fir F3 F4 Fr Taos Trace Reararh Fen Taos Trace Reararh Fen 4 52 Hew Center wor 0253165 uc 5463158 FAD AFFROS FUNE 10 3 03
56. right by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator IV 1 6 Repeated Operations with ANS As many entry answer pairs as the history area shows are stored in memory The last result displayed can be entered on the entry line by pressing 2nd ANS while the last entry computed is entered on the entry line by pressing 2nd ENTRY This makes it easy to use the answer from one computation in another computation For example press 30 15 ENTER so that 45 is the last result displayed Then press 2nd ANS 9 ENTER and get 5 because 45 9 5 The answer locations are indexed by ans where indicates the number of the answer The pairs are numbered with the most recent computation as 1 So the number of a pair changes with each successive computation that is entered The number of an entry or answer can be found by using ZS to scroll up to the entry or answer The number which is the same for both the entry and the answer is shown on the status line To use an earlier answer or entry in a computation to calculate say 15 times answer 3 plus 75 press 15 x 2nd a lock AN S alpha 3 75 ENTER With a function like division you press after you enter an argument For such functions whenever you would start a new calculation with the previous answer followed by pressing the function key you may press just the function key So instead of 2nd ANS 9 in the previous example you could have pressed simply 9 to achieve
57. s it possible to mix degrees and radians in a calculation Execute these keystrokes to calculate tan 45 sin 7 as shown in Figure IV 72 2nd TAN 45 2nd MATH 2 Angle 1 2nd SIN 2nd mT 6 2nd MATH 2 2 ENTER Do you get 1 5 whether your calculator is in either degree mode or in radian mode The degree sign can also be entered by pressing 2nd which saves keystrokes There is no corresponding key for the radian symbol Fir Fer For For Taos Al ebrapCa de Clean Ur Btarnc45 3 sin E Lant4S tsini GI RAD AFFRON FUNC REL Figure IV 72 Angle measure Technology Tip The automatic left parenthesis that the TI 89 places after functions such as sine cosine and tangent as noted in Section IV 1 3 can affect the outcome of calculations In the previous example the degree sign must be inside of the parentheses so that when the TI 89 is in radian mode it calculates the tangent of 45 degrees rather than converting the tangent of 45 radians into an equivalent number of degrees _ T o Also the parentheses around the fraction 6 ae required so that when the TI 89 is in radian mode it converts Ta l l I l 6 into radians rather than converting merely the 6 to radians Experiment with the placement of parentheses to see how they affect the result of computation Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 25 IV 4 2 Graphs of Trigonometric Functions When you
58. sier to press alpha A than to press Kd nine times to get the remain function Fer Fert FY For Fer Fert FY For HATH Clean UF Clean UF Humber exacti Ar List Matrix Complex Statistics reProbability oLTect ri ceilingt oS igni TFF FFF Fha TFF FFF Fh TYFE OF USE 4t4 ENTER OF LESC TYFE OF USE 314 ENTER OF LESC Figure IV 8 MATH menu Figure IV 9 Number sub menu The factorial of a nonnegative integer is the product of all the integers from 1 up to the given integer The symbol for factorial is the exclamation point So 4 pronounced four factorial is 1 2 3 4 24 You will learn more about applications of factorials in your textbook but for now use the TI 89 to calculate 4 The factorial command is located in the MATH menu s Probability sub menu To compute 4 press these keystrokes 4 2nd MATH 7 Probability 1 ENTER On the TI 89 it is possible to do calculations with complex numbers To enter the imaginary number i press 2nd i For example to divide 2 3i by 4 2i press 2 3 2nd i 4 2 2nd i ENTER The result is 0 1 0 87 Figure IV 10 To find the complex conjugate of 4 5i press 2nd MATH 5 Complex 1 conj 4 5 2nd i ENTER Figure IV 10 IV 6 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator Fir Fer Fo For Too Ts Al ebra pla de Clean UF etic Za sl oes Bconjitd 3 4 D HARIH RAD AFFERO
59. ss ENTER twice to go to the matrix previously saved as b which can be edited Return to the home screen and press alpha A 1 x alpha B ENTER to calculate the solution matrix Figure IV 90 The solution is still x 1 y 1 and z 2 Fir Fer For For Too sal ebraycate Clean Ur RAD AFFERO FURL Figure IV 90 Solution matrix IV 7 Sequences IV 7 1 Iteration with the ANS key The ANS feature enables you to perform iteration the process of 1 i 3 for n 27 Then calculate 3 n the answer to the previous calculation Continue to use each answer as n in the next calculation Here are keystrokes to accomplish this iteration on the TI 89 calculator see the results in Figure IV 91 Notice that when you use ANS in place of n in a formula it is sufficient to press ENTER to continue an iteration 1 evaluating a function repeatedly As an example calculate for Iteration Keystrokes Display 1 27 ENTER 2J 2 2nd ANS 1 3 ENTER 8 666666667 3 ENTER 2555050000 4 ENTER 5185185185 Fir Fer Fo For Too Ts Al ebrapla de Clean Ur 2 SEGEGGGGGGGG 1 a Es a 2 II III IIE l 3 22185185185 RAD AFFRON FUNC Figure IV 91 Iteration Press ENTER several more times and see what happens with this iteration You may wish to try it again with a different starting value IV 32 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator IV 7 2 Terms of Sequences Anot
60. t first Then press F1 2 Save Copy As J 1 Data ka KA E MP S alpha 2 ENTER ENTER see Figure V 109 Note that you cannot name the data list TEMPS Now to use the OneVar command you must have the data list TEMPS2 open Then press F5 Calc For the Calculation Type choose 1 OneVar set the x variable to c1 and press ENTER ENTER The TI 89 will calculate several different statistical values The first line represents the mean of the data which is approximately 75 F see Figure IV 112 The second line is the sum of the data the third line is the sum of the squares of the data the IV 38 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator fourth line is the sample standard deviation of the data the fifth line is the number of data values the sixth line is the minimum value of the data the seventh line is the first quartile of the data and the eighth line is the median of the data which is 76 5 F see Figure IV 113 The ninth line is the third quartile of the data and the tenth line is the maximum value of the data ake LE iC a JE resis STAT VARS SAVE COPY OF Crginteres S 7ySigee H9g TYRE ead 67774 Fodder Pdin 6 18 H8 gt variable EEE J 42 soe tee ee aoe CEHE eae Ji 69 Enter SAVe E gt C CANCEL vb Breed 5 18 HH gt 1e 65 69 5 76 5 H RAD AFFRDH FOL Figure IV 113 OneVar command You can scroll through the list of statistical valu
61. the current window s dimensions Later press F2 aloha B 3 ZoomAcl to recall the stored window IV 2 7 Value Graph y x 4x in the standard viewing window Figure IV 18 The TI 89 can calcu late the value of this function for any given x between the xmin and xmax values Press F5 Math to display the Math menu see Figure IV 50 then press 1 Value The graph of the function is displayed and you are prompted to enter a value for x Press 1 ENTER The x value you entered and its corresponding y value are shown at the bottom of the screen and the cursor is located at the point 1 3 on the graph see Figure IV 51 Fir F3 F4 FEr Taos Tracejkedr ar hiai lValue 10 Fir F F4 Fr Taos Trace Reararh Fen 1 Hiniram Maximum Intersection 10 Derivatives SEERIA Inflection a 4 z 6 T S RAD AFFRON FUNC 10 Figure IV 50 Math menu Figure IV 51 Finding a value TYFE OF UZE T CEMTER OF CESC Note that if you have more than one graph on the screen the upper left corner of the TI 89 screen will display the numeral corresponding to the equation of the function in the Y list whose value is being calculated Press FN or kd to move the cursor vertically between functions at the entered x value IV 2 8 Relative Minimums and Maximums Graph y x 4x once again in the standard viewing window This function appears to have a relative minimum near x 1 and a relative maximum near x 1 You may
62. the same result This technique also works for these functions x Here is a situation where this is especially useful Suppose a person makes 5 85 per hour and you are asked to calculate earnings for a day a week and a year Execute the given keystrokes to find the person s incomes during these periods results are shown in Figure IV 7 Pay Period Keystrokes Earnings 8 hour day 5 85 x 8 ENTER 46 80 5 day week x 5 ENTER 234 52 week year x 52 ENTER 12 168 Fir Fer F F For Too sal ebraycate Clean Ur 5 32535 e 46 53 eo ee HAIN RAD AFFERO FUNC Figure IV 7 ANS variable IV 1 7 The MATH Menu Operators and functions associated with a scientific calculator are available either immediately from the keys of the TI 89 or by the 2nd keys You have direct access to common arithmetic operations 2nd V trigonometric functions 2nd SIN 2nd COS 2nd TAN and their inverses K3 SIN K3 COS KA TAN exponential and logarithmic functions 2nd e 2nd LN and a famous constant 2nd 7 A significant difference between the TI 89 graphing calculators and most scientific calculators is that TI 89 requires the argument of a function after the function as you would see in a formula written in your textbook For example on the TI 89 you calculate 16 by pressing the keys 2nd 16 in that order Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 5 Here are keystrokes for basic
63. ther test functions such as lt gt and as well as logic operators can be found on the Test sub menu of the MATH menu IV 12 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator IV 2 4 Graphing a Circle Here is a useful technique for graphs that are not functions but can be split into a top part and a bottom part or into multiple parts Suppose you wish to graph the circle whose equation is x y 36 First solve for y and get an equation for the top semicircle y V36 x and for the bottom semicircle y V36 x Then graph the two semicircles simultaneously Use the following keystrokes to draw the circle s graph First clear any existing functions on the Y screen Enter 36 x as y1 and 36 x as y2 see Figure IV 31 by pressing 2nd V 36 X 2 ENTER 2nd 36 X 2 ENTER Then press KA GRAPH to draw them both Figure IV 32 10 Fir F3 F4 Fr Taos Trace Reagrarh Fen Fir F F4 Tools Edit 7 FLOT vytel3e x2 te ee TE 10 10 y4 Y MAE ELESE HAIN RAD AFFROH FUNC RAD AFFROH FUNC 10 Figure IV 31 Two semicircles Figure IV 32 Circle s graph standard WINDOW If your range were set to the standard viewing window your graph would look like Figure IV 32 Now this does not look like a circle because the units along the axes are not the same This is where the square viewing window is important Press F2 5 and
64. ulation Tere Linked STAT WARS vd x b a 2H1333 TE b 6 559114 Use Frea and Categories MOF ae BBS273 See SOROT aie omer cus ate aide AS seater OO fr anni Garant Enter SAve E gt C CAMCEL USE AWD TO OFEN CHOICE RAD AFF ROK FUR Figure IV 77 Linear regression Figure IV 78 Linear regression model Calculate dialog box Press ENTER to accept the regression equation and close the STAT VARS screen To see both the data points and the regression line Figure IV 79 go to the Plot Setup screen and select Plot 1 then press K3 GRAPH to display the graph 15 Fir F3 F4 Fr Taos Trace Reararh Fen RAD AFFERO FURL Figure IV 79 Linear regression line IV 5 4 Other Regression Models After data points have been entered you can choose from nine different regression models They are all located in the Calc menu of the Data Matrix Editor IV 6 Matrices IV 6 1 Making a Matrix The TI 89 can display and use as many different matrices as the memory will hold I 2 3 9 Here s how to store this 3 x 4 1 3 0 4 matrix in your calculator 2 5 5 17 From the home screen press APPS 6 3 Set the Type to Matrix the Variable to a this is the name of the matrix the Row dimension to 3 and the Col dimension to 4 Figure IV 80 Press ENTER to accept these values F rer F Cel ay Fe lok Setur o a ee TVPG Matrix Fodder mgin variable g_ Row dimension Col dimension H ESC CANCEL r2cil
65. uld have been used for the variable This is the reason that you must indicate to the TI 89 that the variable being used is X Fir Fer For For Tootsil tbra ale Clean UF e colyel24 x7 36 x 17 0h RAD AFFERO FUNC Figure IV 65 solve function Technology Tip To solve an equation like 24x 17 36x you may first rewrite it in general form 24x 36x 17 0 and proceed as above However the solve function does not require that the function be in general form You may also graph the two functions y 24x3 17 and y 36x then zoom and trace to locate their point of intersection IV 22 Copyright by Houghton Mifflin Company All rights reserved TI 89 Graphics Calculator IV 3 3 Solving Systems by Graphing The solutions to a system of equations correspond to the points of intersection of their graphs Figure IV 66 For example to solve the system y 2x 5 andy 2x 1 first graph them together Then use Zoom and Trace or the Intersection option in the Math menu to locate their point of intersection which is 1 3 see Figure IV 67 10 10 Fir F F4 Fr Fir F3 F4 Fr Taos Trace Reararh Fen Taos Trdce Reararh Fen 10 10 10 10 Intersection Horri RAD APFRON FUNC RAD APFROR FUNC 10 10 Figure IV 66 Solving a system of equations Figure IV 67 The point of intersection is 1 3 The solutions of the system of two equations y 2x 5 and y 2x 1 correspond to the solutions of the si
66. use your TI 89 to perform this task Press KA Y above F1 key or APPS 2 Y Editor to display the function editing screen Figure IV 12 You may enter as many as 99 different functions for the TI 89 to use at one time If there is already a function y1 press FN or Ad as many times as necessary to move the cursor to y1 and then press CLEAR to delete whatever was there Then enter the expression 1975 10x by pressing these keys 1975 10 X ENTER Now press HOME Graphing Technology Guide Copyright by Houghton Mifflin Company All rights reserved IV 7 Fir Fer For For Tao Ts AI ebr ala de Clean Ur aS x myles m i1565 LexrSlorot Ltx HAIN RAD AFFRON FUNC HAIN RAD AFFRON FUNC Figure IV 12 Y screen Figure V 13 Evaluating a function Assign the value 2230 to the variable x by using these keystrokes see Figure IV 13 2230 STO gt X ENTER Then press the following keystrokes to evaluate y1 and find January s wages Y 1 X ENTER completes the calculation It is not necessary to repeat all these steps to find the February wages Simply press J to begin editing the previous entry change X to 1865 and press ENTER see Figure IV 13 You may also have TI 89 make a table of values for the function Press KA TblSet to set up the table Figure IV 14 Move the blinking cursor down to the fourth line beside Independent then press gt and 2 ASK ENTER This configuration permits you to input values for x one at a time Now p

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