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 February 15, 2017 28.Dt CACOS 3 29.Os 30.Sh NAME 31.Nm cacos , 32.Nm cacosf , 33.Nm cacosl , 34.Nm cacosh , 35.Nm cacoshf , 36.Nm cacoshl , 37.Nm casin , 38.Nm casinf , 39.Nm casinl , 40.Nm casinh , 41.Nm casinhf , 42.Nm casinhl , 43.Nm catan , 44.Nm catanf , 45.Nm catanl , 46.Nm catanh , 47.Nm catanhf , 48.Nm catanhl 49.Nd complex inverse trigonometric and hyperbolic functions 50.Sh LIBRARY 51.Lb libm 52.Sh SYNOPSIS 53.In complex.h 54.Ft double complex 55.Fn cacos "double complex z" 56.Ft float complex 57.Fn cacosf "float complex z" 58.Ft long double complex 59.Fn cacosl "long double complex z" 60.Ft double complex 61.Fn cacosh "double complex z" 62.Ft float complex 63.Fn cacoshf "float complex z" 64.Ft long double complex 65.Fn cacoshl "long double complex z" 66.Ft double complex 67.Fn casin "double complex z" 68.Ft float complex 69.Fn casinf "float complex z" 70.Ft long double complex 71.Fn casinl "long double complex z" 72.Ft double complex 73.Fn casinh "double complex z" 74.Ft float complex 75.Fn casinhf "float complex z" 76.Ft long double complex 77.Fn casinhl "long double complex z" 78.Ft double complex 79.Fn catan "double complex z" 80.Ft float complex 81.Fn catanf "float complex z" 82.Ft long double complex 83.Fn catanl "long double complex z" 84.Ft double complex 85.Fn catanh "double complex z" 86.Ft float complex 87.Fn catanhf "float complex z" 88.Ft long double complex 89.Fn catanhl "long double complex z" 90.Sh DESCRIPTION 91The 92.Fn cacos , 93.Fn casin , 94and 95.Fn catan 96functions compute the principal value of the inverse cosine, sine, 97and tangent of the complex number 98.Fa z , 99respectively. 100The 101.Fn cacosh , 102.Fn casinh , 103and 104.Fn catanh 105functions compute the principal value of the inverse hyperbolic 106cosine, sine, and tangent. 107The 108.Fn cacosf , 109.Fn casinf , 110.Fn catanf 111.Fn cacoshf , 112.Fn casinhf , 113and 114.Fn catanhf 115functions perform the same operations in 116.Fa float 117precision. 118The 119.Fn cacosl , 120.Fn casinl , 121.Fn catanl 122.Fn cacoshl , 123.Fn casinhl , 124and 125.Fn catanhl 126functions perform the same operations in 127.Fa long double 128precision. 129.Pp 130.ds Un \[cu] 131There is no universal convention for defining the principal values of 132these functions. 133The following table gives the branch cuts, and the 134corresponding ranges for the return values, adopted by the C language. 135.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]" 136.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range 137.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi] 138.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2] 139.It catan Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2] 140.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I] 141.It casinh Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I] 142.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I] 143.El 144.Sh SEE ALSO 145.Xr ccos 3 , 146.Xr ccosh 3 , 147.Xr complex 3 , 148.Xr cos 3 , 149.Xr math 3 , 150.Xr sin 3 , 151.Xr tan 3 152.Sh STANDARDS 153These functions conform to 154.St -isoC-99 . 155