atan2funktiota

The atan2 function, often written as atan2(y, x), is a mathematical function that computes the angle in radians between the positive x-axis and the point (x, y) in the Cartesian plane. It is a two-argument arctangent function, distinguishing it from the single-argument arctangent function, atan(x).

The primary advantage of atan2(y, x) over atan(y/x) is its ability to correctly determine the quadrant of the angle. While atan(y/x) returns values in the range (-pi/2, pi/2), atan2(y, x) returns values in the range (-pi, pi]. This extended range ensures that the function can represent all possible angles. It handles cases where x is zero, which would cause a division by zero error in the single-argument arctangent.

atan2(y, x) is widely used in computer graphics, robotics, and physics for tasks such as calculating the direction of a vector, rotating objects, and determining the orientation of a system. Its ability to provide a precise angle within the full 360 degrees makes it an indispensable tool in many computational applications. The function's behavior is defined such that atan2(y, x) = atan(y/x) when x > 0, atan2(y, x) = atan(y/x) + pi when x < 0 and y >= 0, atan2(y, x) = atan(y/x) - pi when x < 0 and y < 0, atan2(y, x) = pi/2 when x = 0 and y > 0, atan2(y, x) = -pi/2 when x = 0 and y < 0, and atan2(0, 0) is typically undefined or results in zero depending on the implementation.