Answer
$Amplitude = |2| = 2$
$Period = \frac{2\pi}{\frac{1}{2}} = 4\pi$
$Horizontal\ shift = (–\frac{\frac{\pi}{2}}{\frac{1}{2}}) = -\pi$
$Phase = \frac{\pi}{2}$
Work Step by Step
If C is any real number and $B> 0$, then the graphs of $y = A\sin(Bx+C)$ and $y = A\cos (Bx+C)$ will have
$Amplitude = |A|$
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Phase = C$
so for $y = 2\sin (\frac{1}{2}x + \frac{\pi}{2})$
$Amplitude = |2| = 2$
$Period = \frac{2\pi}{\frac{1}{2}} = 4\pi$
$Horizontal\ shift = (–\frac{\frac{\pi}{2}}{\frac{1}{2}}) = -\pi$
$Phase = \frac{\pi}{2}$
