Answer
$y=-\displaystyle \frac{\pi}{2}$
Work Step by Step
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, $y=-\displaystyle \frac{\pi}{2}$
