Symbols:A/Arccotangent
Arccotangent
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 $\openint 0 \pi$.
arccot
- $\arccot$
The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the arccotangent function is $\arccot$.
The $\LaTeX$ code for \(\arccot\) is \arccot .
acot
- $\operatorname {acot}$
A variant symbol used to denote the arccotangent function is $\operatorname {acot}$.
Its $\LaTeX$ code is \operatorname {acot} .
actn
- $\operatorname {actn}$
A variant symbol used to denote the arccotangent function is $\operatorname {actn}$.
Its $\LaTeX$ code is \operatorname {actn} .