# How do you find the exact value of cos^-1(sin((7pi)/2))?

Aug 24, 2015

${\cos}^{-} 1 \left(\sin \left(\frac{7 \pi}{2}\right)\right) = \pi$

#### Explanation:

${\cos}^{-} 1 \left(\sin \left(\frac{7 \pi}{2}\right)\right)$ is

the $t$ in $\left[0 , \pi\right]$ with $\cos t = \sin \left(\frac{7 \pi}{2}\right)$

Since $\sin \left(\frac{7 \pi}{2}\right) = - 1$, we need

the $t$ in $\left[0 , \pi\right]$ with $\cos t = - 1$

So $t = \pi$