mathatan2y

mathatan2y is a two-argument mathematical function used to determine the angle between the positive x-axis and the point (x, y) in the Cartesian plane. It is conceptually equivalent to the standard two-argument arctangent function, commonly written as atan2(y, x). The function returns the angle whose tangent is y/x, but with the correct quadrant determined by the signs of x and y.

In typical implementations, the output is an angle in radians, usually within the range (-pi, pi], though some libraries can return degrees or a different interval. The relationship to polar coordinates is direct: for a point (x, y) with radius r and angle theta, x = r cos(theta) and y = r sin(theta). The mathatan2y function provides theta directly, given y and x (and without requiring r).

Common edge cases include the point (0, 0), for which the angle is undefined in the strict mathematical sense. When x is 0 and y is nonzero, the result is +/- pi/2, depending on the sign of y. When y is 0 and x is positive, the result is 0; when y is 0 and x is negative, the result is pi. Differences in naming or argument order may occur across programming languages, but all versions aim to produce the same angle in the appropriate quadrant.

Applications of mathatan2y include coordinate transformations, robotics navigation, computer graphics, and any domain requiring robust orientation calculations from Cartesian coordinates.