Figure 5-7i shows the graph of y = sin2 3x. a. The function is a sinusoid. Find its

Chapter 5, Problem R.6

(choose chapter or problem)

Figure 5-7i shows the graph of y = sin2 3x. a. The function is a sinusoid. Find its equation from the graph. Confirm algebraically that your equation is correct by using the double argument properties. Figure 5-7i b. Give a numerical counterexample to prove that cos 2x 2 cos x. c. Write an equation expressing cos 2x in terms of cos x alone. Make a table of values to demonstrate that the equation is an identity. d. Write an equation expressing tan 2x in terms of tan x alone. What restrictions are there on the domain of x? e. Suppose that A (360, 450) and sin A = . Find the exact values (no decimals) of cos 2A and cos A. Then calculate the measure of A (no round-off), and find decimal values of cos 2A and cos A directly. How do these answers compare with the exact values? f. Prove that the equation sin 2A = 2 tan A cos2 A is an identity for all the values where both sides are defined. What is the domain of this identity? g. Solve the equation [0, 720] Apply the half argument property to the left side of the equation. What kind of solution did you just give? Plot the graph of the expression on the left side and the graph of y = 0. How many solutions are there? Have you found all of them using both methods? C