atan2

arc tangent function of two variables

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INTERFACE

#include <math.h>

double atan2 ( double y, double x )
long double 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 ( y, ±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:

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

(1)

$$\theta := \mathrm{atan2}(y,x)$$

(2)

STANDARDS

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