# How do you find the exact value of cos^-1(sinpi)?

Sep 7, 2016

$- \frac{\pi}{2}$

#### Explanation:

Use $\sin a = \cos \left(\frac{\pi}{2} - a\right) . \mathmr{and} {f}^{- 1} f \left(x\right) = x$.

Here, the given expression is

${\cos}^{- 1} \left(\sin \pi\right)$

$= {\cos}^{- 1} \left(\cos \left(\frac{\pi}{2} - \pi\right)\right)$

$= \frac{\pi}{2} - \pi$

$= - \frac{\pi}{2}$