Category:Arccotangent Function

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 the arccotangent of $x$ and is written $\arccot x$.

Thus:

The domain of the arccotangent is $\R$

The image of the arccotangent is $\openint 0 \pi$.

Also see

• Category:Arcsine Function
• Category:Arccosine Function
• Category:Arctangent Function
• Category:Arcsecant Function
• Category:Arccosecant Function