Answer
$Period = \frac{2\pi}{\frac{1}{2}} = 4\pi$
$Horizontal\ shift = –\frac{\frac{\pi}{6}}{\frac{1}{2}} = –\frac{\pi}{3}$
$Phase = \frac{\pi}{6}$
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 $y =3 – \sin (\frac{1}{2}x + \frac{\pi}{6})$
$Period = \frac{2\pi}{\frac{1}{2}} = 4\pi$
$Horizontal\ shift = –\frac{\frac{\pi}{6}}{\frac{1}{2}} = –\frac{\pi}{3}$
$Phase = \frac{\pi}{6}$
