| % 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 Abramowitz |
| and Stegun, figure 4.7, 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{ |
| Abramowitz, M. and Stegun, I. A. (1972) |
| \emph{Handbook of Mathematical Functions.} New York: Dover.\cr |
| Chapter 4. Elementary Transcendental Functions: Logarithmic, |
| Exponential, Circular and Hyperbolic Functions |
| } |
| \keyword{math} |