Chapter 6.3, 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 $\frac{\pi }{2}$ 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 with a different horizontal shift, and any cosine curve is also a sine curve. Since 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 $y=a\sin \left(x-b\right)$ or as a cosine curve $y=a\cos \left(x-b\right)$. Explain why you think you have found all possible choices for $a$ and $b$ in each case.