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 $[-3,-1,1]$
