Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.5 - Graphs of Sine and Cosine Functions - Exercise Set - Page 596: 47

Answer

Please see below.
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Work Step by Step

Please note that a cosine function $y=A\cos (Bx-C)$ has amplitude $|A|$, period $\frac{2\pi }{B}$, and phase shift $\frac{C}{B}$. So the function $y=\frac{1}{2}\cos (3x+\frac{\pi }{2})$ has amplitude $|\frac{1}{2}|=\frac{1}{2}$, period $\frac{2\pi }{3 }$, and phase shift $\frac{-\frac{\pi }{2}}{3}=-\frac{\pi }{6}$.
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