Question

How do you graph `y=cos^-1x` over the interval `-1<=x<=1`?

Answer 1

See explanation and graph.

Explanation:

By definition `y = cos^(-1)x in [ 0, pi ]` and

any cosine value `x in [ - 1, 1 }`.

The graph that is a half-wave part of the graph of the inverse

`x = cosy` is confined within the rectangle

#x = - 1, y = 0 , x = 1 and y = pi.

Now see the ( not in uniform scale ) graph,
graph{(y-arccos (x))(y-0.2+0x )(y-3.13 +0.0001y)(x+0.99-0.0001y)(x-1+0.0001y)=0[-1 1 0 3.14]}

See the unrestricted graph `y = (cos)^(-1)x`, using the inverse `x = cos y`.
graph{x-cos y = 0[-1 1 -5 5] }