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 $\closedint 0 \pi$.

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


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

Thus from Inverse of Strictly Monotone Function, $\map g x$ admits an inverse function, which will be continuous and strictly decreasing on $\closedint {-1} 1$.


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


Thus:

The domain of $\arccos x$ is $\closedint {-1} 1$
The image of $\arccos x$ is $\closedint 0 \pi$.

Also see