**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.

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