# How do you find the exact value of sin^-1(sin((7pi)/4))?

$\frac{7 \pi}{4}$
${\sin}^{-} 1 x \textcolor{b l u e}{\text{ is the inverse of }} \sin x$ and in general
$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{f}^{-} 1 \left(f \left(x\right)\right) = x} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
$\Rightarrow {\sin}^{-} 1 \left(\sin \left(\frac{7 \pi}{4}\right)\right) = \frac{7 \pi}{4}$