Answer
$-\frac{\pi}{3}$
Work Step by Step
We need to find the angle between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$.
We know that $\sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$.
Also, $\sin(-x)=-\sin x$
Then $\sin(-\frac{\pi}{3})=-\frac{\sqrt 3}{2}$
The angle is $-\frac{\pi}{3}$.
$\arcsin (-\frac{\sqrt 3}{2})=-\frac{\pi}{3}$