Answer
$\pi$
Work Step by Step
We first write the equation in the form $y=c+a \cos [b(x-d)]$. Therefore, $y=3-6\sin (2x+\frac{\pi}{2})$ becomes $y=3-6\sin [2(x+\frac{\pi}{4})]$.
Comparing the equation to its general form, we find that $b=2$.
We know that the period is equal to $\frac{2\pi}{b}$. Substituting $b=2$ in this formula,
Period$=\frac{2\pi}{2}=\pi$.
