Symbols:A/Arctangent/atan
Arctangent
- $\operatorname {atan}$
From Shape of Tangent Function, we have that $\tan x$ is continuous and strictly increasing on the interval $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.
From the same source, we also have that:
- $\tan x \to + \infty$ as $x \to \dfrac \pi 2 ^-$
- $\tan x \to - \infty$ as $x \to -\dfrac \pi 2 ^+$
Let $g: \openint {-\dfrac \pi 2} {\dfrac \pi 2} \to \R$ be the restriction of $\tan x$ to $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.
Thus from Inverse of Strictly Monotone Function, $\map g x$ admits an inverse function, which will be continuous and strictly increasing on $\R$.
This function is called the arctangent of $x$ and is written $\arctan x$.
Thus:
- The domain of the arctangent is $\R$
- The image of the arctangent is $\openint {-\dfrac \pi 2} {\dfrac \pi 2}$.
A variant symbol used to denote the arctangent function is $\operatorname {atan}$.
The $\LaTeX$ code for \(\operatorname {atan}\) is \operatorname {atan} .
Also denoted as
arctan
- $\arctan$
The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the arctangent function is $\arctan$.
The $\LaTeX$ code for \(\arctan\) is \arctan .
atn
- $\operatorname {atn}$
A variant symbol used to denote the arctangent function is $\operatorname {atn}$.
The $\LaTeX$ code for \(\operatorname {atn}\) is \operatorname {atn} .
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): atan or atn