# What is the graph of y=cos^-1x?

May 21, 2015

Since $y = {\cos}^{-} 1 x$, then $x = \cos y$. So, this graph is a rotation of the cosine wave by 90 degrees. Or at least part of it. Technically if ${\cos}^{-} 1$ of a number gave the output 'n', then it could also give the output n + 360, and several other points along the cosine curve.

However, since this is supposed to be a function, and the ${\cos}^{-} 1$ usually refers to angles less than 360 degrees, we're going to keep it that way so that each x-value only has one y-value assigned to it.

Here's the final graph:
graph{y = arccos x [-4, 4, -1, 4]}
Kind of weird, isn't it? A non-continuous graph!

Because this is the "positive" portion of the cosine curve rotated 90 degrees, it will have a domain (x-value range) of -1 to 1, and a range (y-value range) of 0 to $\pi$.