Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200

CHAPTER 8 Note 8A Changing Mode Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200 For your work in this chapter, check and change, if necessary, three settings. a. Press MODE. In the first line, set Graph to PARAMETRIC. In this chapter you graph and use parametric equations. When you switch to Parametric mode, the Y Editor screen and the Window Editor screen change. b. In the fourth line of the Mode screen, set Angle to DEGREE. You will work with angles in the second half of the chapter and those angles are measured in degrees. If you get a funny answer when using a trigonometric function, check to see that you are still in Degree mode. c. Press [GRAPH] and then press F1 (Tools) 9:Format... Set Graph Order to SIMUL. Often in this chapter you graph more than one set of parametric equations. In Simultaneous mode, all equations graph at the same time. In Sequential mode, equations graph one after the other. Note 8B Graphing in Parametric Mode In Parametric mode, you define equations in terms of the parameter t. To enter the variable t, press T. It takes a pair of equations to create a single parametric graph. Until you define both xt1 and yt1 (or any other x-y pair) on the Y Editor screen, nothing will graph. Setting the Window In Parametric mode the Window Editor screen is different from the familiar Function mode Window Editor screen. The Graph screen that you see is still set by the values of xmin, xmax, xscl, ymin, ymax, and yscl. But in addition, you must set the starting and stopping values for t. The t-values you choose do not affect the dimensions of the Graph screen, but they do affect what will be drawn. tmin the minimum t-value that the calculator uses to evaluate the x- and y-function values. tmax the maximum t-value that the calculator uses to evaluate the x- and y-function values. tstep the increment by which t increases between each evaluation. tstep controls the speed at which the graph is drawn. Start with tstep equal to about one hundredth of the range of t, tmax tmin 1. Ifthe 00 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 8 57

Note 8B Graphing in Parametric Mode TI-89/TI-92 Plus/Voyage 200 graphing speed is not to your liking, or your graph needs more detail, adjust tstep. Setting the Graph Style The graph styles are the same as those in Function mode except there is no shading in parametric equation graphs. See Note 3A for help with graph styles. Note 8C Tracing Parametric Equations In Parametric mode, when you press F3 (Trace) from the Graph screen, the spider starts at the point (x, y) defined by tmin. The t-, x-, and y-values are displayed. Each time you press the right arrow key, t increases by tstep and the spider moves to the new point defined by the new t-value. Note that the right arrow key may not necessarily move the spider to the right on the graph, but it will always increase the value of t. Pressing the left arrow key similarly decreases the value of t. If more than one pair of equations is defined on the Y Editor screen, pressing the up and down arrow keys makes the spider jump to the previous or next pair of equations. When the spider jumps to another pair of equations, the new pair is evaluated at the current t-value. The spider may be anywhere on the screen depending on the x-value and y-value for the new pair of equations. Instead of using the right or left arrow keys to increase or decrease the t-value, you can enter a number. The spider jumps to the point defined by that t-value as long as the number is between tmin and tmax. 58 CHAPTER 8 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 8C Tracing Parametric Equations TI-89/TI-92 Plus/Voyage 200 In Parametric mode there are no commands for finding the intersection of two graphs or the x- or y-intercepts of one graph. You ll need to trace in order to approximate points of intersection. Note 8D Parametric Walk Use the ranger program to collect data for both recorder X and recorder Y. See Note 3C for help with the ranger program. From the ranger Main Menu select 1:Setup/Sample. Use these settings: Realtime No Time (S) 5 Display Distance Begin On [TRIGGER] Button Smoothing None Units Meters Arrow up to Use this setup? and select 1:StartNow. You may now disconnect the CBRs if you wish. Follow the instructions in the investigation; recorders X and Y should press their triggers when the director says go. When finished, reconnect the CBRs and press ENTER. ranger stores time data in a list, l1, and distance data in another list, l2, and it will make an xyline plot of these data. In order to finish the investigation, see Note 1H for help making scatter plots, and see Note 1J for help with linking lists. Clean-Up ranger automatically switches the calculator to Function mode and sets it to display three decimal places. Revisit Note 8A to change to Parametric mode, and, on the Mode screen, set Display Digits to E:FLOAT. Note 8E Drawing Functions While in Parametric mode, the Draw menu allows you to graph a function that uses only x and y. This gives you a way to check your work when eliminating the parameter. For example, follow these steps to graph y 3 2(x 1) at the same time you are displaying parametric equations: a. From the Graph screen, press 2nd [F6] 2:DrawFunc. (On a TI-92 Plus or Voyage 200, press F6.) b. On the Home screen entry line, type 3 2(x 1). c. Press ENTER. Do not press [GRAPH] to display the graph of the function. [ 15.8, 15.8, 1, 7.6, 7.6, 1] Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 8 59

TI-89/TI-92 Plus/Voyage 200 Note 8F Trigonometric and Inverse Trigonometric Functions Before using the trigonometric functions on the calculator, press check that Angle is set to DEGREE. MODE Use 2nd [SIN], 2nd [COS], or 2nd [TAN] to find the sine, cosine, or tangent ratio of any angle measure. (On a TI-92 Plus or Voyage 200, use SIN, COS, or TAN.) In Auto or Exact mode, press [ ] to get the decimal approximation of the ratio. In Approximate mode, press ENTER. See Note 0B for help with changing modes. to In Exact or Approximate mode, press ENTER to get exact ratio values for special angles. For other angles, the calculator gives an equivalent trigonometric expression. Use [SIN 1 ], [COS 1 ],or [TAN 1 ] to find the angle measure that has the given ratio. (On a TI-92 Plus or Voyage 200, use 2nd [SIN 1 ], 2nd [COS 1 ], or 2nd [TAN 1 ].) Note 8G Basketball Free Throw You have two alternatives for doing a basketball simulation. You can manually set up your own simulation or you can use the buckets program. Manual Set-Up Follow these steps to manually set up your own simulation: a. On the Window Editor screen enter tmin 0 tmax 2.1 tstep 0.01 xmin 0 xmax 18.8 xscl 5 ymin 0 ymax 15 yscl 5 60 CHAPTER 8 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 8G Basketball Free Throw TI-89/TI-92 Plus/Voyage 200 b. Store {12,14.5} in a list called xx, and {10,10} in a list called yy. These values represent the x- and y-coordinates of the near and far edges of the basket; you may adjust them according to the data you collect. c. Set up Plot1 to display a scatter plot of (xx,yy) using the square mark. d. On the Y Editor screen enter xt1 v t cos(a) and yt1 16 t 2 v t sin(a) h. Note: You must use a multiplication operation sign between the v and t and between the t and the trigonometric function. e. On the Home screen enter and store values for h, the height (in feet) from which the shot is taken; a, the angle (in degrees) of the shot; and v, the initial velocity (in feet per second) of the shot. Enter all the variable values on the same line, separating each with a colon. f. Display the graph to see your shot. g. From the Home screen press 2nd [ENTRY] to recall the stored variable entries to the entry line. Make any changes you want to the variable values and press ENTER. Display the graph to see your next shot. h. Repeat step g as often as you like. BUCKETS Program Follow these steps to use the premade program: a. On the Y Editor screen scroll up and turn off all plots. b. Type buckets() on the entry line of the Home screen and press ENTER. Note: buckets calls on the program bbbasket in order to run. Both programs must be in your calculator. c. Read the instructions and press ENTER. d. At the prompts, enter values for h, the height (in feet) from which the shot is taken; a, the angle (in degrees) of the shot; and v, the initial velocity (in feet per second) of the shot. Press ENTER after each entry. e. Your shot displays on the screen. If you make it, you ll know it! (Be patient. It takes a while to complete the shot.) Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 8 61

Note 8G Basketball Free Throw TI-89/TI-92 Plus/Voyage 200 f. Press ENTER to see the replay option. Press 1 and ENTER to reenter variable values and try again. Press any other number and ENTER to end the program. Clean-Up After you quit the buckets program, from the Graph screen press 2nd [F6] 1:ClrDraw ENTER to clear the drawing so it won t interfere with future graphing. (On a TI-92 Plus or Voyage 200, press F6.) You may also want to clear all of the equations on the Y Editor screen. Then, from the Graph screen, also press F1 (Tools) 9:Format and turn the axes ON. bbbasket() Prgm Line 13,10,15,10 Line 13,10,13.4,8.6 Line 14.6,10,14.2,8.6 Line 13.4,8.6,14.2,8.6 Line 13.2,9,14.2,9 Line 13.2,9.4,14.4,9.4 Line 13.8,10,13.8,8.6 Line 15,9.4,15,13 DispG EndPrgm buckets() Prgm setmode("graph","parametric") setmode("angle","degree") setgraph("axes","off") main path Define xt1(t)=v*t*cos(a) Define yt1(t)=-16*t^2+v*t*sin(a)+h paths for bounces in special case Define xt2(t)=13*(t-1.05)* cos(70)+13 Define yt2(t)=-16*(t-1.05)^2+13* (t-1.05)*sin(70)+10 Define xt3(t)=5*(t-1.45)* cos(230)+14.8 Define yt3(t)=-16*(t-1.45)^2+5* (t-1.45)*sin(230)+12.4 Define xt4(t)=18*(t-2.2)* cos(100)+12.4 Define yt4(t)=-16*(t-2.2)^2+18* (t-2.2)*sin(100) Define xt5(t)=14*(t-3.3)*cos(100)+9 Define yt5(t)=-16*(t-3.3)^2+14* (t-3.3)*sin(100) Define xt6(t)=11*(t-4.5)*cos(100)+7 62 CHAPTER 8 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 8G Basketball Free Throw TI-89/TI-92 Plus/Voyage 200 (Program: BUCKETS continued) Define yt6(t)=-16*(t-4.5)^2+11* (t-4.5)*sin(100) FnOff 1,2,3,4,5,6 set parameters ClrIO ClrDraw 0átmin 1.5átmax tmaxám.01átstep 0áxmin 18.8áxmax 5áxscl 0áymin 12.4áymax 5áyscl instructions Disp "Your objective is to get" Disp "the SWISH message." Disp "" Disp "Press ENTER to set the" Disp "ball's path and again" Disp "after the ball stops." Pause If t 2.2 Goto lbl5 If t 3.3 Goto lbl6 If t 4.5 Goto lbl7 PtOn xt6(t),yt6(t) Lbl lbl7 PtOn xt5(t),yt5(t) Lbl lbl6 PtOn xt4(t),yt4(t) Lbl lbl5 PtOn xt3(t),yt3(t) If t=1.9 Text "It's GOOD!!!" Lbl lbl4 PtOn xt2(t),yt2(t) standard loop Lbl lbl3 PtOn xt1(t),yt1(t) draw basket on graph screen bbbasket() begin try Lbl lbl2 ClrIO Disp "height, h" Disp "angle, a" Disp "velocity, v" Prompt h,a,v 0át Lbl lbl1 If h 5 or a 60 or v 25 not special case Goto lbl3 special case of hitting front rim 5.5ám If t 1.05 Goto lbl3 If t 1.45 Goto lbl4 advance t Lbl lbl9.02+tát If abs(13.75-xt1(t)).35 and abs(10-yt1(t)).1 Then in center of rim Text "SWISH!" EndIf If t m Goto lbl1 path is drawn Pause Disp "AGAIN? (1=YES)" Input choice If choice=1 Goto lbl2 DispHome EndPrgm Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 8 63

TI-89/TI-92 Plus/Voyage 200 Note 8H Graphing with Boolean Expressions A Boolean expression is a statement with an equality or inequality that is either true or false. The calculator evaluates Boolean expressions and displays whether they are true or false. The calculator can use Boolean expressions in conjunction with the when( command to turn on or turn off part of an equation depending on the value of a variable. See Note 4G for more information about Boolean expressions and for help with the when( command. For example, the equations xt1 3t and yt1 when(t 20,5 t,5) graph the horizontal line y 5 for t-values less than 20 because the Boolean expression t 20 is false. For t-values greater than or equal to 20, the Boolean expression becomes true, so yt1 5 t is turned on and the graph jumps to the diagonal line y 1 x 3 5. Here is what happens when tmin 0, tmax 50, and tstep 0.1. [0, 150, 10, 0, 50, 5] In these screens, the lines appear as if they will collide, but they nicely bypass each other because part of the yt1 and yt2 equations are turned on at the right time. [0, 900, 100, 0, 2, 1] [0, 900, 100, 0, 2, 1] 64 CHAPTER 8 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200