Given the and coordinates of a point, returns the angle associated with the point in radians. If the point’s -coordinate is negative, meaning that the point is in quadrant or , the function returns a negative angle.
|A number representing the vertical component of a point in the Cartesian Plane
|A number representing the horizontal component of a point in the Cartesian Plane
The improved arctangent function takes in a and coordinate as input and returns the angle associated with the point . For example, given the point as input the function returns the angle of . This is illustrated by figure below.
= atan2( 1, 1) = 0.785... // (1/8)*TAU
Many programming languages provide both the
tan2 function and the
atan function. The difference between the two functions is the range of possible return values for real number input. The range of is while the range of is . In other words, the
atan function returns angles on the right half of the circle and
atan2 returns angles on the whole circle.
The different behavior is visualized below in the second quadrant when given the same point as input. The
atan2 function returns the corresponding angle that is greater than a perpendicular while the
atan function returns the corresponding angle that is less than a perpendicular angle.
One way to reconcile the difference between the two functions is to extend the input of
atan to accept numbers in the complex number system. In this case, the
atan function will return angles on the full circle.