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% File src/library/base/man/Hyperbolic.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2011 R Core Team
% Distributed under GPL 2 or later

\name{Hyperbolic}
\title{Hyperbolic Functions}
\usage{
cosh(x)
sinh(x)
tanh(x)
acosh(x)
asinh(x)
atanh(x)
}
\alias{cosh}
\alias{sinh}
\alias{tanh}
\alias{acosh}
\alias{asinh}
\alias{atanh}
\description{
  These functions give the obvious hyperbolic functions.  They
  respectively compute the hyperbolic cosine, sine, tangent, and their
  inverses, arc-cosine, arc-sine, arc-tangent (or \sQuote{\emph{area cosine}},
  etc).
}
\arguments{
   \item{x}{a numeric or complex vector}
}
\details{
   These are \link{internal generic} \link{primitive} functions: methods
   can be defined for them individually or via the
   \code{\link[=S3groupGeneric]{Math}} group generic.

   Branch cuts are consistent with the inverse trigonometric functions
   \code{asin} \emph{et seq}, and agree with those defined in
   \bibcitet{|R:Abramowitz+Stegun:1972|figure 4.7 on page 86}.
   The behaviour actually on the cuts
   follows the C99 standard which requires continuity coming round the
   endpoint in a counter-clockwise direction.
}
\section{S4 methods}{
  All are S4 generic functions: methods can be defined
  for them individually or via the
  \code{\link[=S4groupGeneric]{Math}} group generic.
}
\seealso{
  The trigonometric functions, \code{\link{cos}}, \code{\link{sin}},
  \code{\link{tan}}, and their inverses
  \code{\link{acos}}, \code{\link{asin}}, \code{\link{atan}}.

  The logistic distribution function \code{\link{plogis}} is a shifted
  version of \code{tanh()} for numeric \code{x}.
}
\references{
  \bibinfo{R:Abramowitz+Stegun:1972}{footer}{Chapter 4. Elementary
    Transcendental Functions: Logarithmic, Exponential, Circular and
    Hyperbolic Functions}
  \bibshow{*}
}
\keyword{math}