How to have the arctan2 / atan2 function in LaTeX?

amsmath provides \DeclareMathOperator{\foo}{foo} to define new operator names that are typeset similar to \sin and \cos, \ln, i.e. upright font and correct spacings.

This can be used with \atantwo as well (the 2 isn't allowed as part of the macro name, however, therefor \atantwo.

\documentclass{article}

\usepackage{amsmath}

\DeclareMathOperator{\atantwo}{atan2}

\DeclareMathOperator{\arctantwo}{arctan2}


\begin{document}

\[
\atantwo ( y, x)
\]

\[
\arctantwo ( y, x)
\]



\[
\sin (x y)
\]



\end{document}

Note: The atan2(y,x) function determines the angle in polar coordinates and is related to but different than the function atan(y/x). The two are not interchangeable. The atan function has output range (-pi/2,pi/2), whereas atan2 has an output range of (-pi,pi]. If x>0, then atan2(y,x)=atan(y/x). If x<0, then atan2(y,x)=atan(y/x) +/- pi. And if x=0 then atan(y/x) is undefined while atan2(y,x)=pi/2 for y>0 or -pi/2 for y<0. This definition of atan2 (or equivalently arctan2) is the same both for mathematics and for common programming languages including C, FORTRAN, and matlab.

If you want you can let them be a little bit more intelligent to enable \atan2 and \arctan2

\long\def\gobbleone#1{}
\protected\def\atan{\futurelet\tmptoken\doatan}
\protected\def\doatan{\operatorname{atan\ifx\tmptoken22\fi}%
  \ifx\tmptoken2\expandafter\gobbleone\fi}
\protected\def\arctan{\futurelet\tmptoken\doarctan}
\protected\def\doarctan{\operatorname{arc\,tan\ifx\tmptoken22\fi}%
  \ifx\tmptoken2\expandafter\gobbleone\fi}

$\atan2(y, x) \arctan2(y, x) \sin(x, y)$