Precalculus (6th Edition) Blitzer

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

Chapter 10 - Section 10.1 - Sequences and Summation Notation - Exercise Set - Page 1051: 106

Answer

amplitude $\frac{1}{2}$, period $\frac{2\pi}{3}$, phase $-\frac{\pi}{6}$, see graph
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Work Step by Step

Step 1. Given $y=\frac{1}{2}cos(3x+\frac{\pi}{2})=\frac{1}{2}cos3(x+\frac{\pi}{6})$ we can identify its amplitude as $|A|=\frac{1}{2}$, period as $p=\frac{2\pi}{3}$, and phase shift as $\phi=-\frac{\pi}{6}$. Step To graph the function, start from $y=\frac{1}{2}sin(x)$, shift $\frac{\pi}{6}$ to the left, then shrink horizontally by a factor of $3$ as shown in the figure.
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