Chapter 5.3, Problem 90E

DISCUSS: Sinusoidal Curves The graph of y = sin x is the same as the graph of y = cos x shifted to the right π/2 units. So the sine curve y = sin x is also at the same time a cosine curve: $y=\cos \left(x-\frac{\pi }{2}\right)$. In fact, any sine curve is also a cosine curve with a different horizontal shift, and any cosine curve is also a sine curve. Sine and cosine curves are collectively referred to as sinusoidal. For the curve whose graph is shown, find all possible ways of expressing it as a sine curve y = a sin(x − b) or as a cosine curve y = a cos(x − b). Explain why you think you have found all possible choices for a and b in each case.