atan2 overview

The atan2 function computes the principal value of the arc tangent of y / x, using the signs of both arguments to determine the quadrant of the return value. It produces correct results even when the resulting angle is near π/2 or -π/2 (or x near 0).

The atan2 function is used mostly to convert from rectangular (x,y) to polar (r, θ) coordinates that must satisfy x = r cos(θ) and y = r sin (θ). In general, conversions to polar coordinates should be computed thus

• atan2 ( ±0, -0) returns ± π.
• atan2 ( ±0, +0 ) returns ±0.
• atan2 ( ±0, x ) returns ±π for x < 0.
• atan2 ( ±0 , x ) returns ±0 for x > 0.
• atan2 ( ±0 ) returns -π/2 for y > 0.
• atan2 ( ±y, -∞ ) returns ±π for finite y > 0.
• atan2 ( ±y, +∞ ) returns ±0 for finite y > 0.
• atan2 ( ±∞, +x ) returns ±π/2 for finite x.
• atan2 ( ±∞, -∞ ) returns ±3π/4.
• atan2 ( ±∞, +∞ ) returns ±π/4.