155 lines
4.2 KiB
Groff
155 lines
4.2 KiB
Groff
.\" Copyright (c) 2013 David Schultz <das@FreeBSD.org>
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" $FreeBSD$
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.\"
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.Dd February 15, 2017
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.Dt CACOS 3
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.Os
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.Sh NAME
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.Nm cacos ,
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.Nm cacosf ,
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.Nm cacosl ,
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.Nm cacosh ,
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.Nm cacoshf ,
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.Nm cacoshl ,
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.Nm casin ,
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.Nm casinf ,
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.Nm casinl ,
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.Nm casinh ,
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.Nm casinhf ,
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.Nm casinhl ,
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.Nm catan ,
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.Nm catanf ,
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.Nm catanl ,
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.Nm catanh ,
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.Nm catanhf ,
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.Nm catanhl
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.Nd complex inverse trigonometric and hyperbolic functions
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In complex.h
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.Ft double complex
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.Fn cacos "double complex z"
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.Ft float complex
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.Fn cacosf "float complex z"
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.Ft long double complex
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.Fn cacosl "long double complex z"
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.Ft double complex
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.Fn cacosh "double complex z"
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.Ft float complex
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.Fn cacoshf "float complex z"
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.Ft long double complex
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.Fn cacoshl "long double complex z"
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.Ft double complex
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.Fn casin "double complex z"
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.Ft float complex
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.Fn casinf "float complex z"
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.Ft long double complex
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.Fn casinl "long double complex z"
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.Ft double complex
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.Fn casinh "double complex z"
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.Ft float complex
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.Fn casinhf "float complex z"
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.Ft long double complex
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.Fn casinhl "long double complex z"
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.Ft double complex
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.Fn catan "double complex z"
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.Ft float complex
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.Fn catanf "float complex z"
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.Ft long double complex
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.Fn catanl "long double complex z"
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.Ft double complex
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.Fn catanh "double complex z"
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.Ft float complex
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.Fn catanhf "float complex z"
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.Ft long double complex
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.Fn catanhl "long double complex z"
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.Sh DESCRIPTION
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The
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.Fn cacos ,
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.Fn casin ,
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and
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.Fn catan
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functions compute the principal value of the inverse cosine, sine,
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and tangent of the complex number
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.Fa z ,
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respectively.
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The
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.Fn cacosh ,
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.Fn casinh ,
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and
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.Fn catanh
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functions compute the principal value of the inverse hyperbolic
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cosine, sine, and tangent.
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The
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.Fn cacosf ,
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.Fn casinf ,
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.Fn catanf
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.Fn cacoshf ,
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.Fn casinhf ,
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and
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.Fn catanhf
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functions perform the same operations in
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.Fa float
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precision.
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The
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.Fn cacosl ,
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.Fn casinl ,
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.Fn catanl
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.Fn cacoshl ,
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.Fn casinhl ,
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and
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.Fn catanhl
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functions perform the same operations in
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.Fa long double
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precision.
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.Pp
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.ds Un \[cu]
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There is no universal convention for defining the principal values of
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these functions.
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The following table gives the branch cuts, and the
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corresponding ranges for the return values, adopted by the C language.
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.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]"
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.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range
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.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi]
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.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2]
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.It catan Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2]
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.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I]
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.It casinh Ta (-\*(If*I, -I) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I]
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.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I]
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.El
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.Sh SEE ALSO
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.Xr ccos 3 ,
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.Xr ccosh 3 ,
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.Xr complex 3 ,
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.Xr cos 3 ,
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.Xr math 3 ,
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.Xr sin 3 ,
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.Xr tan 3
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.Sh STANDARDS
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These functions conform to
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.St -isoC-99 .
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