atan2funktio

atan2funktio, commonly written as atan2, is the two-argument arctangent function used in mathematics and computing. It takes two real inputs, traditionally written as y and x, and returns the angle θ in radians such that tan θ = y/x, with θ placed in the correct quadrant based on the signs of x and y. Unlike the plain arctan of y/x, atan2 uses both arguments to resolve the quadrant of the resulting angle.

The function returns the polar angle of the point (x, y) relative to the positive x-axis. Equivalently, if r = sqrt(x^2 + y^2), then cos θ = x/r and sin θ = y/r. The usual range of atan2 is the interval [-π, π], with π returned when y = 0 and x < 0. When x = 0, the value is ±π/2 depending on the sign of y. When y = 0 and x > 0, the result is 0. In the degenerate case (x, y) = (0, 0), the result is undefined in strict mathematics; some implementations return 0 or NaN.

Common applications include converting Cartesian coordinates to polar coordinates, determining headings or bearings in robotics and navigation, and handling angle calculations in computer graphics. In code, the function is typically invoked as atan2(y, x). The result is provided in radians, so conversion to degrees may be used if needed.

Examples: atan2(1, 1) ≈ π/4; atan2(1, -1) ≈ 3π/4; atan2(-1, -1) ≈ -3π/4; atan2(0, -1) = π. Understanding the two-argument form helps avoid quadrant errors that occur with the single-argument arctan.