Sketching the function $y=\cos^{-1}\cos(x)$ for $x\in\mathbb{R}$

 YouTube Video Link:  YOUTUBE CHANNEL

Question: Sketch $y=\cos^{-1}\cos x$ for $x\in\mathbb{R}$.

Basically you work it out for $0 \le x \le \pi$ first, which is fairly easy just using the definition of the inverse cosine function. Then you can use symmetry to guess the rest. 

Below we did work out the details for  $\pi \le x \le 2\pi$ and since the function has period $2\pi$ we know the rest of the graph.

The YouTube video talks through the basic step.

Below is a screen shot from the YouTube video for this problem.