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atan2

Arc tangent function of two variables

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Contents

Interface
Description
Special Values
Notes
See Also
Standards
Page Comments

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 $\pi/2$ or $-\pi/2$ (for x near 0).

Example 1:

#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;
}

Output:

The arc tangent ratio of 0.166667 is 0.165149

Special Values

atan2 ( ±0, -0 ) returns ± $\pi$ .
atan2 ( ±0, +0 ) returns ±0.
atan2 ( ±0, x ) returns ± $\pi$ for x < 0. \n atan2 ( \a ±0, \a 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, $\theta$ ) coordinates that must satisfy $x=r \cos(\theta)$ and $y=r \sin(\theta)$ . In general, conversions to polar coordinates should be computed thus:

(1)

$r := \sqrt{x^2 + y^2}$