Category:Arccotangent Function

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This category contains results about Arccotangent Function.


Arccotangent Function

From Shape of Cotangent Function, we have that $\cot x$ is continuous and strictly decreasing on the interval $\openint 0 \pi$.

From the same source, we also have that:

$\cot x \to + \infty$ as $x \to 0^+$
$\cot x \to - \infty$ as $x \to \pi^-$


Let $g: \openint 0 \pi \to \R$ be the restriction of $\cot x$ to $\openint 0 \pi$.

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


This function is called arccotangent of $x$ and is written $\arccot x$.

Thus:

The domain of $\arccot x$ is $\R$
The image of $\arccot x$ is $\openint 0 \pi$.