# FreeBSD Manual Pages

```ATAN2(3)		 BSD Library Functions Manual		      ATAN2(3)

NAME
atan2, atan2f -- arc tangent functions of two variables

LIBRARY
Math Library (libm, -lm)

SYNOPSIS
#include <math.h>

double
atan2(double y, double x);

float
atan2f(float y, float x);

DESCRIPTION
The atan2() and the atan2f() functions compute the	principal value	of the
arc tangent of y/x, using the signs of both arguments to determine	the

RETURN VALUES
The atan2() and the atan2f() functions, if	successful, return the arc
tangent of	y/x in the range [-pi, +pi] radians.  If both x	and y are
zero, the global variable errno is	set to EDOM.  On the VAX:

atan2(y, x) :=	  atan(y/x)			  if x > 0,
sign(y)*(pi -	atan(|y/x|))	  if x < 0,
0				  if x = y = 0,	or
sign(y)*pi/2			  if x = 0 != y.

NOTES
The function atan2() defines "if x	> 0," atan2(0, 0) = 0 on a VAX despite
that previously atan2(0, 0) may have generated an error message.  The
reasons for assigning a value to atan2(0, 0) are these:

1.	Programs that test arguments to	avoid computing	atan2(0, 0)
must be	indifferent to its value.  Programs that require it to
be invalid are vulnerable to diverse reactions to that inva-
lidity on diverse computer systems.

2.	The atan2() function is	used mostly to convert from rectangu-
lar (x,y) to polar (r,theta) coordinates that must satisfy x =
r*cos theta and	y = r*sin theta.  These	equations are satis-
fied when (x=0,y=0) is mapped to (r=0,theta=0) on a VAX.  In
general, conversions to	polar coordinates should be computed
thus:

r	   := hypot(x,y);  ... := sqrt(x*x+y*y)
theta	:= atan2(y,x).

3.	The foregoing formulas need not	be altered to cope in a	rea-
sonable	way with signed	zeros and infinities on	a machine that
conforms to IEEE 754; the versions of hypot(3) and atan2()
provided for such a machine are	designed to handle all cases.
That is	why atan2(+-0, -0) = +-pi for instance.	 In general
the formulas above are equivalent to these:

r	:= sqrt(x*x+y*y); if r = 0 then	x := copysign(1,x);