CodeCogs

arc tangent function of two variables

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

Workings

\code #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
", (y/x), result); return 0; } \endcode

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: