Category:Arccosine Function

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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 $\left[{0 \,.\,.\, \pi}\right]$.