Answer
$Period = \frac{2\pi}{\frac{1}{3}} = 6\pi$
$Horizontal\ shift = –\frac{–\frac{\pi}{6}}{\frac{1}{3}} = \frac{\pi}{2}$
$Phase = –\frac{\pi}{6}$
Work Step by Step
If C is any real number and $B> 0$, then the graphs of $y = \sin(Bx+C)$ and $y = \cos (Bx+C)$ will have
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Phase = C$
so for $y =2 + \cos (\frac{1}{3}x – \frac{\pi}{6})$
$Period = \frac{2\pi}{\frac{1}{3}} = 6\pi$
$Horizontal\ shift = –\frac{–\frac{\pi}{6}}{\frac{1}{3}} = \frac{\pi}{2}$
$Phase = –\frac{\pi}{6}$
