How can one graph arccos(x) on paper?

Question

The question is : Sketch the graph of arccos(x) clearly showing the axes intercepts and endpoints.

Answer 1

The graph of $f^{-1}$ is the graph of $f$ mirrored at the line $y = x$.

$P=(x, y=f(x))$ turns into $P'(x) = (y, x)$.

So if you know $f(x) = \cos(x)$ you know how to sketch $f^{-1}(x) = \arccos(x)$.

(Large version)

Note that a function is not allowed to map any argument $x$ to more than one value $y=f(x)$. The mirrored graph of $\cos$ must be restricted to some interval to not violate that property.