Answer
$\dfrac{\sqrt{2}}{2}$
Work Step by Step
Divide both sides by $4$ to obtain:
$\sin^{-1}{x} = \dfrac{\pi}{4}$
Recall:
$y = \sin^{-1}{x} \hspace{15pt} \to \hspace{15pt} x = \sin{y}$
$\text{where } \hspace{15pt} -1 \leq x \leq 1 \hspace{15pt} \text{and} \hspace{15pt} -\dfrac{\pi}{2} \leq y \leq \dfrac{\pi}{2}$
Thus,
$\sin^{-1}{x}=\dfrac{\pi}{4} \rightarrow x = \sin{\dfrac{\pi}{4}}$
$x =\sin{\dfrac{\pi}{4}} = \boxed{\dfrac{\sqrt{2}}{2}}$
