Answer
$\displaystyle \frac{\pi}{4}$
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 $y=\displaystyle \frac{\pi}{4}$ such that $\displaystyle \sin(\frac{\pi}{4}) =\displaystyle \frac{\sqrt{2}}{2}$
so
$y= \displaystyle \sin^{-1}(\frac{\sqrt{2}}{2})=\frac{\pi}{4}$
