Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 6 - The Circular Functions and Their Graphs - 6.4 Translations of the Graphs of the Sine and Cosine Functions - 6.4 Exercises - Page 613: 31

Answer

amplitude $\frac{1}{4}$, period $ 4\pi$, no vertical translation, and phase shift $\pi$ to the left.

Work Step by Step

Given $y=-\frac{1}{4}\ cos(\frac{1}{2}x+\frac{\pi}{2})=-\frac{1}{4}\ cos\frac{1}{2}(x+\pi)$, we can find the following: amplitude $\frac{1}{4}$, period $p=\frac{2\pi}{1/2}=4\pi$, no vertical translation, and phase shift $\pi$ to the left.
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