Answer
$-\displaystyle \frac{\pi}{3}$
Work Step by Step
Inverse Sine Function
$y=\sin^{-1}x$ or $y=$ arcsin $x$ means that
$x=\sin y$, for $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$.
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In the interval $-\displaystyle \frac{\pi}{2} \leq y \leq \frac{\pi}{2}$
we find $y=-\displaystyle \frac{\pi}{3}$ such that $\displaystyle \sin(-\frac{\pi}{3}) =-\displaystyle \frac{\sqrt{3}}{2}$
so
$y=$ arcsin$(-\displaystyle \frac{\sqrt{3}}{2})=-\frac{\pi}{3}$
