# Category:Arccosine Function

This category contains results about Arccosine Function.

Arccosine Function

From Shape of Cosine Function, we have that $\cos x$ is continuous and strictly decreasing on the interval $\left[{0 \,.\,.\, \pi}\right]$.

From Cosine of Multiple of Pi, $\cos \pi = -1$ and $\cos 0 = 1$.

Therefore, let $g: \left[{0 \,.\,.\, \pi}\right] \to \left[{-1 \,.\,.\, 1}\right]$ be the restriction of $\cos x$ to $\left[{0 \,.\,.\, \pi}\right]$.

Thus from Inverse of Strictly Monotone Function, $g \left({x}\right)$ admits an inverse function, which will be continuous and strictly decreasing on $\left[{-1 \,.\,.\, 1}\right]$.

This function is called arccosine of $x$ and is written $\arccos x$.

Thus:

• The domain of $\arccos x$ is $\left[{-1 \,.\,.\, 1}\right]$
• The image of $\arccos x$ is $\left[{0 \,.\,.\, \pi}\right]$.

## Pages in category "Arccosine Function"

The following 9 pages are in this category, out of 9 total.