SITE-C teams: Lesson 15

Do an analysis of the function g(x) = cos^{2} x - sin x.

Turn on the **CASIO CFX-9850G** by pressing

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