Answer
$Period = \frac{2\pi}{4} = \frac{\pi}{2}$
$Horizontal\ shift = –\frac{\pi}{4} = –\frac{\pi}{4}$ (Negative meaning left shift)
$Phase = \pi$
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 $y = \sin (4x + \pi)$
$Period = \frac{2\pi}{4} = \frac{\pi}{2}$
$Horizontal\ shift = –\frac{\pi}{4} = –\frac{\pi}{4}$
Negative meaning left shift
$Phase = \pi$
