1.\" Copyright (c) 2013 David Schultz <das@FreeBSD.org> 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 13.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 14.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 17.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 19.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 20.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 21.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 22.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 23.\" SUCH DAMAGE. 24.\" 25.\" $FreeBSD$ 26.\" 27.Dd May 27, 2013 28.Dt CACOS 3 29.Os 30.Sh NAME 31.Nm cacos , 32.Nm cacosf , 33.Nm cacosh , 34.Nm cacoshf , 35.Nm casin , 36.Nm casinf 37.Nm casinh , 38.Nm casinhf 39.Nm catan , 40.Nm catanf 41.Nm catanh , 42.Nm catanhf 43.Nd complex arc trigonometric and hyperbolic functions 44.Sh LIBRARY 45.Lb libm 46.Sh SYNOPSIS 47.In complex.h 48.Ft double complex 49.Fn cacos "double complex z" 50.Ft float complex 51.Fn cacosf "float complex z" 52.Ft double complex 53.Fn cacosh "double complex z" 54.Ft float complex 55.Fn cacoshf "float complex z" 56.Ft double complex 57.Fn casin "double complex z" 58.Ft float complex 59.Fn casinf "float complex z" 60.Ft double complex 61.Fn casinh "double complex z" 62.Ft float complex 63.Fn casinhf "float complex z" 64.Ft double complex 65.Fn catan "double complex z" 66.Ft float complex 67.Fn catanf "float complex z" 68.Ft double complex 69.Fn catanh "double complex z" 70.Ft float complex 71.Fn catanhf "float complex z" 72.Sh DESCRIPTION 73The 74.Fn cacos , 75.Fn casin , 76and 77.Fn catan 78functions compute the principal value of the inverse cosine, sine, 79and tangent of the complex number 80.Fa z , 81respectively. 82The 83.Fn cacosh , 84.Fn casinh , 85and 86.Fn catanh 87functions compute the principal value of the inverse hyperbolic 88cosine, sine, and tangent. 89The 90.Fn cacosf , 91.Fn casinf , 92.Fn catanf 93.Fn cacoshf , 94.Fn casinhf , 95and 96.Fn catanhf 97functions perform the same operations in 98.Fa float 99precision. 100.Pp 101.ie '\*[.T]'utf8' 102. ds Un \[cu] 103.el 104. ds Un U 105. 106There is no universal convention for defining the principal values of 107these functions. The following table gives the branch cuts, and the 108corresponding ranges for the return values, adopted by the C language. 109.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]" 110.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range 111.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi] 112.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2] 113.It catan Ta (-\*(If*I, -i) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2] 114.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I] 115.It casinh Ta (-\*(If*I, -i) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I] 116.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I] 117.El 118.Sh SEE ALSO 119.Xr ccos 3 , 120.Xr ccosh 3 , 121.Xr complex 3 , 122.Xr cos 3 , 123.Xr math 3 , 124.Xr sin 3 , 125.Xr tan 3 126.Sh STANDARDS 127These functions conform to 128.St -isoC-99 . 129