# How do you evaluate cos^-1[cos(-pi/2)]?

Apr 13, 2018

$\frac{\pi}{2}$

#### Explanation:

Cosine is an even function, meaning $\cos \left(- x\right) = \cos x$.

So, $\cos \left(- \frac{\pi}{2}\right) = \cos \left(\frac{\pi}{2}\right) = 0$

Then, we really want

${\cos}^{-} 1 \left(0\right) = x \to \cos \left(x\right) = 0 \to x = \frac{\pi}{2}$ as the domain of the inverse cosine is $\left[- 1 , 1\right]$.

Apr 13, 2018

#### Explanation:

check the attached picture.