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.Dd February 15, 2017 26.Dt CACOS 3 27.Os 28.Sh NAME 29.Nm cacos , 30.Nm cacosf , 31.Nm cacosl , 32.Nm cacosh , 33.Nm cacoshf , 34.Nm cacoshl , 35.Nm casin , 36.Nm casinf , 37.Nm casinl , 38.Nm casinh , 39.Nm casinhf , 40.Nm casinhl , 41.Nm catan , 42.Nm catanf , 43.Nm catanl , 44.Nm catanh , 45.Nm catanhf , 46.Nm catanhl 47.Nd complex inverse trigonometric and hyperbolic functions 48.Sh LIBRARY 49.Lb libm 50.Sh SYNOPSIS 51.In complex.h 52.Ft double complex 53.Fn cacos "double complex z" 54.Ft float complex 55.Fn cacosf "float complex z" 56.Ft long double complex 57.Fn cacosl "long double complex z" 58.Ft double complex 59.Fn cacosh "double complex z" 60.Ft float complex 61.Fn cacoshf "float complex z" 62.Ft long double complex 63.Fn cacoshl "long double complex z" 64.Ft double complex 65.Fn casin "double complex z" 66.Ft float complex 67.Fn casinf "float complex z" 68.Ft long double complex 69.Fn casinl "long double complex z" 70.Ft double complex 71.Fn casinh "double complex z" 72.Ft float complex 73.Fn casinhf "float complex z" 74.Ft long double complex 75.Fn casinhl "long double complex z" 76.Ft double complex 77.Fn catan "double complex z" 78.Ft float complex 79.Fn catanf "float complex z" 80.Ft long double complex 81.Fn catanl "long double complex z" 82.Ft double complex 83.Fn catanh "double complex z" 84.Ft float complex 85.Fn catanhf "float complex z" 86.Ft long double complex 87.Fn catanhl "long double complex z" 88.Sh DESCRIPTION 89The 90.Fn cacos , 91.Fn casin , 92and 93.Fn catan 94functions compute the principal value of the inverse cosine, sine, 95and tangent of the complex number 96.Fa z , 97respectively. 98The 99.Fn cacosh , 100.Fn casinh , 101and 102.Fn catanh 103functions compute the principal value of the inverse hyperbolic 104cosine, sine, and tangent. 105The 106.Fn cacosf , 107.Fn casinf , 108.Fn catanf 109.Fn cacoshf , 110.Fn casinhf , 111and 112.Fn catanhf 113functions perform the same operations in 114.Fa float 115precision. 116The 117.Fn cacosl , 118.Fn casinl , 119.Fn catanl 120.Fn cacoshl , 121.Fn casinhl , 122and 123.Fn catanhl 124functions perform the same operations in 125.Fa long double 126precision. 127.Pp 128.ds Un \[cu] 129There is no universal convention for defining the principal values of 130these functions. 131The following table gives the branch cuts, and the 132corresponding ranges for the return values, adopted by the C language. 133.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]" 134.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range 135.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi] 136.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2] 137.It catan Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2] 138.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I] 139.It casinh Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I] 140.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I] 141.El 142.Sh SEE ALSO 143.Xr ccos 3 , 144.Xr ccosh 3 , 145.Xr complex 3 , 146.Xr cos 3 , 147.Xr math 3 , 148.Xr sin 3 , 149.Xr tan 3 150.Sh STANDARDS 151These functions conform to 152.St -isoC-99 . 153