Modified tangent function

Question

I remember reading once of a modified arctangent function which was suited to be a chart on the circle. It should be defined something like

$$\theta(x,y)=\begin{cases} \arctan(\frac{y}{x}) & x>0\\ \pi/2 & (x,y)=(0,1)\\ -\pi/2 & (x,y)=(0,-1)\\ \pi+\arctan(\frac{y}{x}) & x<0, y>0\\ -\pi+\arctan(\frac{y}{x}) & x<0, y<0 \end{cases}$$

Can somebody remind me of its name?

Answer 1

It appears to be known as $atan2(y,x)$ (the two-argument arctangent function).

https://en.wikipedia.org/wiki/Atan2