## Precalculus (6th Edition)

$y=-\displaystyle \frac{\pi}{2}$
By definition of arcsin, y is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ such that $\sin y=-1.$ $\displaystyle \sin(-\frac{\pi}{2})=-1$, and $-\displaystyle \frac{\pi}{2}\in[-\frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ so, $y=-\displaystyle \frac{\pi}{2}$