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arc tangent function of two variables

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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 $\pi/2$ or $-\pi/2$ (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;
}

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:

$r:= hypot(x,y) :=\sqrt{x^2 + y^2}$

(1)

$\theta := atan2(y,x)$

(2)

STANDARDS

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