## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 4 - Section 4.5 - Graphs of Sine and Cosine Functions - Exercise Set - Page 598: 115

#### Answer

a. $[-\frac{\pi}{6},\frac{23\pi}{6},\frac{\pi}{6}]$ by $[-5,1,1]$ b. $[-\frac{\pi}{6},\frac{7\pi}{6},\frac{\pi}{6}]$ by $[-3,-1,1]$

#### Work Step by Step

a. As a sine function oscillates within $[-1,1]$, we can find the range of the given function as $[-5,1]$. The phase shift of the function is $\phi=-\frac{\pi}{6}$ and its period is $p=2\pi$ so $2p=\frac{24\pi}{6}$; thus we can set the viewing rectangle as $[-\frac{\pi}{6},\frac{23\pi}{6},\frac{\pi}{6}]$ by $[-5,1,1]$ b. As a sine function oscillates within $[-1,1]$, we can find the range of the given function as $[-3,-1]$. The phase shift of the function is $\phi=-\frac{\pi}{6}$ and its period is $p=\frac{2\pi}{3}$, so $2p=\frac{8\pi}{6}$; thus we can set the viewing rectangle as $[-\frac{\pi}{6},\frac{7\pi}{6},\frac{\pi}{6}]$ by $[-3,-1,1]$

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