Answer
-3
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 $y=3-6\sin [2(x+\frac{\pi}{4})]$.
The y-intercept of a graph is found by substituting $x=0$ in the equation. Therefore,
$y=3-6\sin [2(x+\frac{\pi}{4})]$
$y=3-6\sin [2(0+\frac{\pi}{4})]$
$y=3-6\sin [2(\frac{\pi}{4})]$
$y=3-6\sin [\frac{\pi}{2}]$
$y=3-6(1)$
$y=3-6$
$y=-3$
Therefore, the y-intercept is -3.