SITE-C teams: Lesson 15

 

Do an analysis of the function g(x) = cos2 x - sin x.

Turn on the CASIO CFX-9850G by pressing AC/ON.

Use the cursor arrows to highlight the GRAPH menu and press EXE or just press 5 when at the main menu screen.

In the Y1 slot enter ( cos X )2 - sin X and press EXE to store it in memory.

Press SHIFT MENU (SETUP), use the down cursor arrow to scroll down and highlight the Angle line, press F2 (Rad) EXIT. Since the sin x and cos x are periodic functions with period 2p , g(x) is also.

Press SHIFT F3 (V-Window) to set the parameters as follows:

Xmin = 0

Xmax = 2p

Xscale = p /2

Ymin = -2

Ymax = 2

Yscale = 1

Note that the calculator converts 2p and p /2 to their decimal equivalent as soon as EXE is pressed.

Press EXIT to return to the function list. Make sure that no other Y-slot is highlighted, i.e. selected for drawing. Press F6 (DRAW) to see the graph.

Press SHIFT F5 (G-Solv) F3 (MIN) to obtain the first local minimum at (1.570797326, -1) or (p /2, -1). Press the right cursor arrow to find the second local minimum at (4.71238898, 1) or (3p /2, 1).

Press SHIFT F5 (G-Solv) F2 (MAX) to obtain the first local maximum at (3.665191429, 1.25) or (7p /6, 1.25). Press the right cursor arrow to find the second local maximum at (5.759586531, 1.25) or (11p /6, 1.25).

Press EXIT to return to the function list and in slot Y2 enter the following:

OPTN F2 (CALC) F1 (d/dX) VARS F4 (GRPH) F1 (Y) 1 , X ) EXE. To help distinguish graphs use the up cursor arrow to highlight Y2 and press F4 (COLR) F3 (Grn) EXIT. Press F6 (DRAW) to see the graph of g(x) and g(x).

Press F5 (G-Solv) F1 (ROOT) and the down cursor arrow to display Y2 on the screen. Press EXE to find the first root at (1.570797326, 0) and note that the x value is the x value for the first local minimum. Press the right cursor arrow to find the second root at (3.665191429, 0) and note that the x value is the x value for the first local maximum. Press the right cursor arrow to find the third root at (4.71238898, 0) and note that the x value is the x value for the second local minimum. Press the right cursor arrow again to find the fourth root at (5.759586531, 0) and note that the x value is the x value for the second local maximum.

Press EXIT MENU.

Turn off the CASIO CFX-9850G by pressing SHIFT AC/ON (OFF).