1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
|
.\" Copyright (c) 2013 David Schultz <das@FreeBSD.org>
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" $FreeBSD$
.\"
.Dd February 15, 2017
.Dt CACOS 3
.Os
.Sh NAME
.Nm cacos ,
.Nm cacosf ,
.Nm cacosl ,
.Nm cacosh ,
.Nm cacoshf ,
.Nm cacoshl ,
.Nm casin ,
.Nm casinf ,
.Nm casinl ,
.Nm casinh ,
.Nm casinhf ,
.Nm casinhl ,
.Nm catan ,
.Nm catanf ,
.Nm catanl ,
.Nm catanh ,
.Nm catanhf ,
.Nm catanhl
.Nd complex inverse trigonometric and hyperbolic functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn cacos "double complex z"
.Ft float complex
.Fn cacosf "float complex z"
.Ft long double complex
.Fn cacosl "long double complex z"
.Ft double complex
.Fn cacosh "double complex z"
.Ft float complex
.Fn cacoshf "float complex z"
.Ft long double complex
.Fn cacoshl "long double complex z"
.Ft double complex
.Fn casin "double complex z"
.Ft float complex
.Fn casinf "float complex z"
.Ft long double complex
.Fn casinl "long double complex z"
.Ft double complex
.Fn casinh "double complex z"
.Ft float complex
.Fn casinhf "float complex z"
.Ft long double complex
.Fn casinhl "long double complex z"
.Ft double complex
.Fn catan "double complex z"
.Ft float complex
.Fn catanf "float complex z"
.Ft long double complex
.Fn catanl "long double complex z"
.Ft double complex
.Fn catanh "double complex z"
.Ft float complex
.Fn catanhf "float complex z"
.Ft long double complex
.Fn catanhl "long double complex z"
.Sh DESCRIPTION
The
.Fn cacos ,
.Fn casin ,
and
.Fn catan
functions compute the principal value of the inverse cosine, sine,
and tangent of the complex number
.Fa z ,
respectively.
The
.Fn cacosh ,
.Fn casinh ,
and
.Fn catanh
functions compute the principal value of the inverse hyperbolic
cosine, sine, and tangent.
The
.Fn cacosf ,
.Fn casinf ,
.Fn catanf
.Fn cacoshf ,
.Fn casinhf ,
and
.Fn catanhf
functions perform the same operations in
.Fa float
precision.
The
.Fn cacosl ,
.Fn casinl ,
.Fn catanl
.Fn cacoshl ,
.Fn casinhl ,
and
.Fn catanhl
functions perform the same operations in
.Fa long double
precision.
.Pp
.ds Un \[cu]
There is no universal convention for defining the principal values of
these functions.
The following table gives the branch cuts, and the
corresponding ranges for the return values, adopted by the C language.
.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]"
.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range
.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi]
.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2]
.It catan Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2]
.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I]
.It casinh Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I]
.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I]
.El
.Sh SEE ALSO
.Xr ccos 3 ,
.Xr ccosh 3 ,
.Xr complex 3 ,
.Xr cos 3 ,
.Xr math 3 ,
.Xr sin 3 ,
.Xr tan 3
.Sh STANDARDS
These functions conform to
.St -isoC-99 .
|
