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ATAN2(3)		    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  rectan-
		  gular	(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 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);

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").

FreeBSD	14.3			 July 31, 2008			      ATAN2(3)

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