## Precalculus: Mathematics for Calculus, 7th Edition

$\Rightarrow \sin ^{-1}\left( \sin \left( \dfrac {3\pi }{4}\right) \right) =\sin ^{-1}\left( \sin \left( \dfrac {\pi }{4}\right) \right) =\dfrac {\pi }{4}$
$\sin ^{-1}\left( \sin x\right) =x\left( -\dfrac {\pi }{2}\leq x\leq \dfrac {\pi }{2}\right)$ $\dfrac {3\pi }{4} > \dfrac {\pi }{2}$ so we need to convert it $\sin \dfrac {3\pi }{4}=\sin \dfrac {\pi }{4}$ $\Rightarrow \sin ^{-1}\left( \sin \left( \dfrac {3\pi }{4}\right) \right) =\sin ^{-1}\left( \sin \left( \dfrac {\pi }{4}\right) \right) =\dfrac {\pi }{4}$