# How do you find the value of cos^ -1(0) ?

${\cos}^{- 1} 0 = \frac{\pi}{2}$
${\cos}^{- 1}$ is an angle $x$, for which $\cos x = 0$. If you look at the graph of $f \left(x\right) = \cos x$ you see that $\cos x = 0$ for $x = \frac{\pi}{2} + k \pi$ for any $k \in \mathbb{Z}$, so the smallest positive value is $\frac{\pi}{2}$