Answer
$-60^{o}$
Work Step by Step
Solve for radians, then convert to degrees.
$y=\sin^{-1}x =\arcsin x$
Domain: $[-1, 1] $
Range: $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$
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$y$ is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ such that $\displaystyle \sin y=-\frac{\sqrt{3}}{2}$
$\displaystyle \sin(-\frac{\pi}{3})=-\frac{\sqrt{3}}{2}\qquad$and$\displaystyle \quad -\frac{\pi}{3}\in[-\frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$,
so
$y =-\displaystyle \frac{\pi}{3}$
To convert radians to degrees, multiply y with $\displaystyle \frac{180^{o}}{\pi}$
$\displaystyle \theta=-\frac{\pi}{3}\cdot\frac{180^{o}}{\pi}=-60^{o}$
