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:

Example - Arc tangent function of two variables

Workings

#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;
}

Solution

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.

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, $\theta$ ) coordinates that must satisfy $x=r \cos(\theta)$ and $y=r \sin(\theta)$ . In general, conversions to polar coordinates should be computed thus: