# atan2(3) [osx man page]

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

NAME
atan2 -- arc tangent function of two variables

SYNOPSIS
#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.

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, +-0) returns -pi/2 for y < 0.

atan2(+-y, -infinity) returns +-pi for finite y > 0.

atan2(+-y, +infinity) returns +-0 for finite y > 0.

atan2(+-infinity, x) returns +-pi/2 for finite x.

atan2(+-infinity, -infinity) returns +-3*pi/4.

atan2(+-infinity, +infinity) 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*x+y*y)
theta     := atan2(y,x).

VECTOR OPERATIONS
If you need to apply the atan2() function to SIMD vectors or arrays, using the following functions provided by the Accelerate.framework may
give significantly better performance:

#include <Accelerate/Accelerate.h>

vFloat atan2f(vFloat y, vFloat x);
void vvatan2f(float *z, const float *y, const float *x, const int *n);
void vvatan2(double *z, const double *y, const double *x, const int *n);

SEE ALSO
acos(3), asin(3), atan(3), cos(3), cosh(3), sin(3), sinh(3), tan(3), tanh(3), math(3),

STANDARDS
The atan2() function conforms to ISO/IEC 9899:2011.

BSD								 December 11, 2006							       BSD```

## Check Out this Related Man Page

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

NAME
atan2, atan2f, atan2l, carg, cargf, cargl -- arc tangent and complex phase angle functions

LIBRARY
Math Library (libm, -lm)

SYNOPSIS
#include <math.h>

double
atan2(double y, double x);

float
atan2f(float y, float x);

long double
atan2l(long double y, long double x);

#include <complex.h>

double
carg(double complex z);

float
cargf(float complex z);

long double
cargl(long double complex z);

DESCRIPTION
The atan2(), atan2f(), and atan2l() functions compute the principal value of the arc tangent of y/x, using the signs of both arguments to
determine the quadrant of the return value.

The carg(), cargf(), and cargl() functions compute the complex argument (or phase angle) of z.  The complex argument is the number theta such
that z = r * e^(I * theta), where r = cabs(z).  The call carg(z) is equivalent to atan2(cimag(z), creal(z)), and similarly for cargf() and
cargl().

RETURN VALUES
The atan2(), atan2f(), and atan2l() functions, if successful, return the arc tangent of y/x in the range [-pi, +pi] radians.  Here are some
of the special cases:

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 despite that previously atan2(0, 0) may have generated an error message.	The rea-
sons 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 invalidity on diverse computer systems.

2.	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.  These equations are satisfied when (x=0,y=0) is mapped to (r=0,theta=0).  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 reasonable 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);

SEE ALSO
acos(3), asin(3), atan(3), cabs(3), cos(3), cosh(3), math(3), sin(3), sinh(3), tan(3), tanh(3)

STANDARDS
The atan2(), atan2f(), atan2l(), carg(), cargf(), and cargl() functions conform to ISO/IEC 9899:1999 (``ISO C99'').

BSD								   July 31, 2008							       BSD```
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