Answer
$y=-\frac{\pi}{2}$
Work Step by Step
RECALL:
$y=\arcsin{x} \longrightarrow \sin{y}=x$, $y$ is in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$
Note that $\sin {(\frac{\pi}{2})}=1$.
Since sine is an odd function, $\sin{(-x)}=-\sin{x}$.
Thus, $\sin{(-\frac{\pi}{2})}=-\sin{(\frac{\pi}{2})}=-1$
Therefore,
$y=\arcsin{(-1)}\longrightarrow y=-\frac{\pi}{2}$
