As $x$ runs over $[0, 1]$, which values does $\cos^{-1} x$ take?

Explanation

1. 01

   $\cos^{-1}$ is decreasing: $\cos^{-1} 0 = \frac{\pi}{2}$ and $\cos^{-1} 1 = 0$.

2. 02

   So it takes every value from 0 to $\frac{\pi}{2}$.