# How do you find the exact value of sin^-1(sin(pi/5))?

$\frac{\pi}{5}$
The functions ${\sin}^{-} 1 x \text{ and} \sin x$ are $\textcolor{b l u e}{\text{inverse}}$ and in general.
$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{f}^{-} 1 \left(f \left(x\right)\right) = x} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
$\Rightarrow {\sin}^{-} 1 \left(\sin \left(\frac{\pi}{5}\right)\right) = \frac{\pi}{5}$