# How do you evaluate sin^-1(sin((7pi)/10))?

Feb 26, 2017

$\frac{7 \pi}{10}$

#### Explanation:

Recall that ${\sin}^{-} 1 \left(x\right)$ is the inverse of $\sin \left(x\right)$

Recall that a composition of inverse functions returns the independent variable.

${f}^{-} 1 \left(f \left(x\right)\right) = x$

So, if $f \left(x\right) = \sin \left(\frac{7 \pi}{10}\right)$ and ${f}^{-} 1 \left(x\right) = {\sin}^{-} 1 \left(f \left(x\right)\right)$

then ${f}^{-} 1 \left(f \left(x\right)\right) = {\sin}^{-} 1 \left(\sin \left(\frac{7 \pi}{10}\right)\right) = \frac{7 \pi}{10}$