arctan2( y , x )

The inverse tangent in SageMath of the ratio of planar coordinates y and x taking quadrant into account. Alias of atan2.

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:

Series expansions about the origin:

Special values:

Related functions:   atan2   arctan

Function category: circular functions sagemath-docs