arctanxy1xy

arctanxy1xy is a mathematical function that is a variant of the arctangent function, which is the inverse of the tangent function. The arctangent function, often denoted as atan2(y, x) in programming languages, computes the angle θ in the Euclidean plane, given the coordinates (x, y) of a point. This function is particularly useful in trigonometry and vector mathematics.

The function atan2(y, x) returns the angle θ such that -π ≤ θ ≤ π, and it correctly determines the quadrant of the angle based on the signs of x and y. This is in contrast to the standard arctangent function, atan(y/x), which only returns angles in the range -π/2 ≤ θ ≤ π/2 and does not account for the quadrant.

The atan2(y, x) function is defined as follows:

atan2(y, x) = {

arctan(y/x) if x > 0,

arctan(y/x) + π if x < 0 and y ≥ 0,

arctan(y/x) - π if x < 0 and y < 0,

+π/2 if x = 0 and y > 0,

-π/2 if x = 0 and y < 0

}

This function is widely used in various fields, including computer graphics, robotics, and navigation systems, where it is essential for determining the orientation and direction of objects or vehicles in a coordinate plane.