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32.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91
33.\" $Id: atan2.3,v 1.6 2006/06/13 18:55:19 scanon Exp $
34.\"
35.Dd December 11, 2006
36.Dt ATAN2 3
37.Os
38.Sh NAME
39.Nm atan2
40.Nd arc tangent function of two variables
41.Sh SYNOPSIS
42.Fd #include <math.h>
43.Ft double
44.Fn atan2 "double y" "double x"
45.Ft long double
46.Fn atan2l "long double y" "long double x"
47.Ft float
48.Fn atan2f "float y" "float x"
49.Sh DESCRIPTION
50The
51.Fn atan2
52function computes the principal value of the arc tangent of
53.Ar y/ Ns Ar x ,
54using the signs of both arguments to determine the quadrant of
55the return value.
56.Sh SPECIAL VALUES
57.Fn atan2 "�0, -0"
58returns �pi.
59.Pp
60.Fn atan2 "�0, +0"
61returns �0.
62.Pp
63.Fn atan2 "�0, x"
64returns �pi for x < 0.
65.Pp
66.Fn atan2 "�0, x"
67returns �0 for x > 0.
68.Pp
69.Fn atan2 "y, �0"
70returns +pi/2 for y > 0.
71.Pp
72.Fn atan2 "y, �0"
73returns -pi/2 for y < 0.
74.Pp
75.Fn atan2 "�y, -infinity"
76returns �pi for finite y > 0.
77.Pp
78.Fn atan2 "�y, +infinity"
79returns �0 for finite y > 0.
80.Pp
81.Fn atan2 "�infinity, x"
82returns �pi/2 for finite x.
83.Pp
84.Fn atan2 "�infinity, -infinity"
85returns �3*pi/4.
86.Pp
87.Fn atan2 "�infinity, +infinity"
88returns �pi/4.
89.Sh NOTES
90The
91.Fn atan2
92function is used mostly to convert from rectangular (x,y)
93to polar
94.if n\
95(r,theta)
96.if t\
97(r,\(*h)
98coordinates that must satisfy x =
99.if n\
100r\(**cos theta
101.if t\
102r\(**cos\(*h
103and y =
104.if n\
105r\(**sin theta.
106.if t\
107r\(**sin\(*h.
108In general, conversions to polar coordinates
109should be computed thus:
110.Bd -unfilled -offset indent
111.if n \{\
112r := hypot(x,y); ... := sqrt(x\(**x+y\(**y)
113theta := atan2(y,x).
114.\}
115.if t \{\
116r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
117\(*h := atan2(y,x).
118.\}
119.Ed
120.Sh SEE ALSO
121.Xr acos 3 ,
122.Xr asin 3 ,
123.Xr atan 3 ,
124.Xr cos 3 ,
125.Xr cosh 3 ,
126.Xr sin 3 ,
127.Xr sinh 3 ,
128.Xr tan 3 ,
129.Xr tanh 3 ,
130.Xr math 3 ,
131.Sh STANDARDS
132The
133.Fn atan2
134function conforms to ISO/IEC 9899:1999(E).