atan2

Name

atan2

Interface

#include <math.h>

double	atan2 (double y, double x)
long	atan2l (long double y, long double x)
float	atan2f (float y, float x)

Description

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 or (x near 0).

Example:

#include <stdio.h>
#include <math.h>
 
int main(void)
{
  double result, x=90.0, y=15.0;
  result = atan2(y, x);
  printf("The arc tangent ratio of %lf is %lf\n", (y/x), result);
  return 0;
}

Special Values

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

Notes

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

(1)

(2)

See Also

acos, asin, atan, cos, cosh, sin, sinh, tan, tanh

Standards

The atan2 function conforms to ISO/IEC 9899:1999(E).