atan2( y , x )

The inverse tangent in SageMath of the ratio of planar coordinates y and x taking quadrant into account. Alias of arctan2.

The function arctan returns values in the range $$\left( -\frac{\pi}{2} , \frac{\pi}{2} \right)$$. By using separate signed arguments, this function returns values in the full range $$( -\pi , \pi )$$ of the coordinate plane.

Plot on the real axis: