1e4afa19cSDavid Schultz.\" Copyright (c) 2013 David Schultz <das@FreeBSD.org> 2e4afa19cSDavid Schultz.\" All rights reserved. 3e4afa19cSDavid Schultz.\" 4e4afa19cSDavid Schultz.\" Redistribution and use in source and binary forms, with or without 5e4afa19cSDavid Schultz.\" modification, are permitted provided that the following conditions 6e4afa19cSDavid Schultz.\" are met: 7e4afa19cSDavid Schultz.\" 1. Redistributions of source code must retain the above copyright 8e4afa19cSDavid Schultz.\" notice, this list of conditions and the following disclaimer. 9e4afa19cSDavid Schultz.\" 2. Redistributions in binary form must reproduce the above copyright 10e4afa19cSDavid Schultz.\" notice, this list of conditions and the following disclaimer in the 11e4afa19cSDavid Schultz.\" documentation and/or other materials provided with the distribution. 12e4afa19cSDavid Schultz.\" 13e4afa19cSDavid Schultz.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 14e4afa19cSDavid Schultz.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15e4afa19cSDavid Schultz.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16e4afa19cSDavid Schultz.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 17e4afa19cSDavid Schultz.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18e4afa19cSDavid Schultz.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 19e4afa19cSDavid Schultz.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 20e4afa19cSDavid Schultz.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 21e4afa19cSDavid Schultz.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 22e4afa19cSDavid Schultz.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 23e4afa19cSDavid Schultz.\" SUCH DAMAGE. 24e4afa19cSDavid Schultz.\" 251fdfb24aSMahdi Mokhtari.Dd February 15, 2017 26e4afa19cSDavid Schultz.Dt CACOS 3 27e4afa19cSDavid Schultz.Os 28e4afa19cSDavid Schultz.Sh NAME 29e4afa19cSDavid Schultz.Nm cacos , 30e4afa19cSDavid Schultz.Nm cacosf , 311fdfb24aSMahdi Mokhtari.Nm cacosl , 32e4afa19cSDavid Schultz.Nm cacosh , 33e4afa19cSDavid Schultz.Nm cacoshf , 341fdfb24aSMahdi Mokhtari.Nm cacoshl , 35e4afa19cSDavid Schultz.Nm casin , 361fdfb24aSMahdi Mokhtari.Nm casinf , 371fdfb24aSMahdi Mokhtari.Nm casinl , 38e4afa19cSDavid Schultz.Nm casinh , 391fdfb24aSMahdi Mokhtari.Nm casinhf , 401fdfb24aSMahdi Mokhtari.Nm casinhl , 41e4afa19cSDavid Schultz.Nm catan , 421fdfb24aSMahdi Mokhtari.Nm catanf , 431fdfb24aSMahdi Mokhtari.Nm catanl , 44e4afa19cSDavid Schultz.Nm catanh , 451fdfb24aSMahdi Mokhtari.Nm catanhf , 461fdfb24aSMahdi Mokhtari.Nm catanhl 471fdfb24aSMahdi Mokhtari.Nd complex inverse trigonometric and hyperbolic functions 48e4afa19cSDavid Schultz.Sh LIBRARY 49e4afa19cSDavid Schultz.Lb libm 50e4afa19cSDavid Schultz.Sh SYNOPSIS 51e4afa19cSDavid Schultz.In complex.h 52e4afa19cSDavid Schultz.Ft double complex 53e4afa19cSDavid Schultz.Fn cacos "double complex z" 54e4afa19cSDavid Schultz.Ft float complex 55e4afa19cSDavid Schultz.Fn cacosf "float complex z" 561fdfb24aSMahdi Mokhtari.Ft long double complex 571fdfb24aSMahdi Mokhtari.Fn cacosl "long double complex z" 58e4afa19cSDavid Schultz.Ft double complex 59e4afa19cSDavid Schultz.Fn cacosh "double complex z" 60e4afa19cSDavid Schultz.Ft float complex 61e4afa19cSDavid Schultz.Fn cacoshf "float complex z" 621fdfb24aSMahdi Mokhtari.Ft long double complex 631fdfb24aSMahdi Mokhtari.Fn cacoshl "long double complex z" 64e4afa19cSDavid Schultz.Ft double complex 65e4afa19cSDavid Schultz.Fn casin "double complex z" 66e4afa19cSDavid Schultz.Ft float complex 67e4afa19cSDavid Schultz.Fn casinf "float complex z" 681fdfb24aSMahdi Mokhtari.Ft long double complex 691fdfb24aSMahdi Mokhtari.Fn casinl "long double complex z" 70e4afa19cSDavid Schultz.Ft double complex 71e4afa19cSDavid Schultz.Fn casinh "double complex z" 72e4afa19cSDavid Schultz.Ft float complex 73e4afa19cSDavid Schultz.Fn casinhf "float complex z" 741fdfb24aSMahdi Mokhtari.Ft long double complex 751fdfb24aSMahdi Mokhtari.Fn casinhl "long double complex z" 76e4afa19cSDavid Schultz.Ft double complex 77e4afa19cSDavid Schultz.Fn catan "double complex z" 78e4afa19cSDavid Schultz.Ft float complex 79e4afa19cSDavid Schultz.Fn catanf "float complex z" 801fdfb24aSMahdi Mokhtari.Ft long double complex 811fdfb24aSMahdi Mokhtari.Fn catanl "long double complex z" 82e4afa19cSDavid Schultz.Ft double complex 83e4afa19cSDavid Schultz.Fn catanh "double complex z" 84e4afa19cSDavid Schultz.Ft float complex 85e4afa19cSDavid Schultz.Fn catanhf "float complex z" 861fdfb24aSMahdi Mokhtari.Ft long double complex 871fdfb24aSMahdi Mokhtari.Fn catanhl "long double complex z" 88e4afa19cSDavid Schultz.Sh DESCRIPTION 89e4afa19cSDavid SchultzThe 90e4afa19cSDavid Schultz.Fn cacos , 91e4afa19cSDavid Schultz.Fn casin , 92e4afa19cSDavid Schultzand 93e4afa19cSDavid Schultz.Fn catan 94e4afa19cSDavid Schultzfunctions compute the principal value of the inverse cosine, sine, 95e4afa19cSDavid Schultzand tangent of the complex number 96e4afa19cSDavid Schultz.Fa z , 97e4afa19cSDavid Schultzrespectively. 98e4afa19cSDavid SchultzThe 99e4afa19cSDavid Schultz.Fn cacosh , 100e4afa19cSDavid Schultz.Fn casinh , 101e4afa19cSDavid Schultzand 102e4afa19cSDavid Schultz.Fn catanh 103e4afa19cSDavid Schultzfunctions compute the principal value of the inverse hyperbolic 104e4afa19cSDavid Schultzcosine, sine, and tangent. 105e4afa19cSDavid SchultzThe 106e4afa19cSDavid Schultz.Fn cacosf , 107e4afa19cSDavid Schultz.Fn casinf , 108e4afa19cSDavid Schultz.Fn catanf 109e4afa19cSDavid Schultz.Fn cacoshf , 110e4afa19cSDavid Schultz.Fn casinhf , 111e4afa19cSDavid Schultzand 112e4afa19cSDavid Schultz.Fn catanhf 113e4afa19cSDavid Schultzfunctions perform the same operations in 114e4afa19cSDavid Schultz.Fa float 115e4afa19cSDavid Schultzprecision. 1161fdfb24aSMahdi MokhtariThe 1171fdfb24aSMahdi Mokhtari.Fn cacosl , 1181fdfb24aSMahdi Mokhtari.Fn casinl , 1191fdfb24aSMahdi Mokhtari.Fn catanl 1201fdfb24aSMahdi Mokhtari.Fn cacoshl , 1211fdfb24aSMahdi Mokhtari.Fn casinhl , 1221fdfb24aSMahdi Mokhtariand 1231fdfb24aSMahdi Mokhtari.Fn catanhl 1241fdfb24aSMahdi Mokhtarifunctions perform the same operations in 1251fdfb24aSMahdi Mokhtari.Fa long double 1261fdfb24aSMahdi Mokhtariprecision. 127e4afa19cSDavid Schultz.Pp 128e4afa19cSDavid Schultz.ds Un \[cu] 129e4afa19cSDavid SchultzThere is no universal convention for defining the principal values of 1301fdfb24aSMahdi Mokhtarithese functions. 1311fdfb24aSMahdi MokhtariThe following table gives the branch cuts, and the 132e4afa19cSDavid Schultzcorresponding ranges for the return values, adopted by the C language. 133e4afa19cSDavid Schultz.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]" 134e4afa19cSDavid Schultz.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range 135e4afa19cSDavid Schultz.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi] 136e4afa19cSDavid Schultz.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2] 137*d592c356SEitan Adler.It catan Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2] 138e4afa19cSDavid Schultz.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I] 139*d592c356SEitan Adler.It casinh Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I] 140e4afa19cSDavid Schultz.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I] 141e4afa19cSDavid Schultz.El 142e4afa19cSDavid Schultz.Sh SEE ALSO 143e4afa19cSDavid Schultz.Xr ccos 3 , 144e4afa19cSDavid Schultz.Xr ccosh 3 , 145e4afa19cSDavid Schultz.Xr complex 3 , 146e4afa19cSDavid Schultz.Xr cos 3 , 147e4afa19cSDavid Schultz.Xr math 3 , 148e4afa19cSDavid Schultz.Xr sin 3 , 149e4afa19cSDavid Schultz.Xr tan 3 150e4afa19cSDavid Schultz.Sh STANDARDS 151e4afa19cSDavid SchultzThese functions conform to 152e4afa19cSDavid Schultz.St -isoC-99 . 153