Answer
$-\frac{\pi}{3}$
Work Step by Step
RECALL:
$y=\arcsin{x} \longrightarrow \sin{y}=x$ where $y$ is in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$.
Note that:
$\sin{(\frac{\pi}{3})} = \frac{\sqrt3}{2}$
Since sine is an dd function, then $\sin{(-\theta)} = -\sin{\theta}$.
Thus,
$\sin{(-\frac{\pi}{3})} = -\sin{(\frac{\pi}{3})}=-\frac{\sqrt3}{2}$
Therefore, the solution to the given equation is $-\frac{\pi}{3}$.
