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

Aug 7, 2018

See explanation and graph.

#### Explanation:

By definition $y = {\cos}^{- 1} x \in \left[0 , \pi\right]$ and

any cosine value $x \in \left[- 1 , 1\right\}$.

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

$x = \cos y$ 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 $y = {\left(\cos\right)}^{- 1} x$, using the inverse $x = \cos y$.
graph{x-cos y = 0[-1 1 -5 5] }