\HeaderA{Hyperbolic}{Hyperbolic Functions}{Hyperbolic}
\aliasA{acosh}{Hyperbolic}{acosh}
\aliasA{asinh}{Hyperbolic}{asinh}
\aliasA{atanh}{Hyperbolic}{atanh}
\aliasA{cosh}{Hyperbolic}{cosh}
\aliasA{sinh}{Hyperbolic}{sinh}
\aliasA{tanh}{Hyperbolic}{tanh}
\keyword{math}{Hyperbolic}
\begin{Description}\relax
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 \dQuote{\emph{area cosine}},
etc).
\end{Description}
\begin{Usage}
\begin{verbatim}
cosh(x)
sinh(x)
tanh(x)
acosh(x)
asinh(x)
atanh(x)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] a numeric or complex vector
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
These are generic functions: methods can be defined for them
individually or via the \code{\LinkA{Math}{Math}} group generic.

Branch cuts are consistent with the inverse trigonometric functions
\code{asin()} et seq, and agree with those defined in Abramowitz and
Stegun, figure 4.7, page 86.
\end{Details}
\begin{References}\relax
Abramowitz, M. and Stegun, I. A. (1972)
\emph{Handbook of Mathematical Functions.} New York: Dover.\\
Chapter 4. Elementary Transcendental Functions: Logarithmic,
Exponential, Circular and Hyperbolic Functions
\end{References}
\begin{SeeAlso}\relax
The trigonometric functions, \code{\LinkA{cos}{cos}}, \code{\LinkA{sin}{sin}},
\code{\LinkA{tan}{tan}}, and their inverses
\code{\LinkA{acos}{acos}}, \code{\LinkA{asin}{asin}}, \code{\LinkA{atan}{atan}}.

The logistic distribution function \code{\LinkA{plogis}{plogis}} is a shifted
version of \code{tanh()} for numeric \code{x}.
\end{SeeAlso}

