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.