% File src/library/base/man/Trig.Rd
% Part of the R package, http://www.R-project.org
% Copyright 1995-2007 R Core Development Team
% Distributed under GPL 2 or later

\name{Trig}
\alias{Trig}
\alias{cos}
\alias{sin}
\alias{tan}
\alias{acos}
\alias{asin}
\alias{atan}
\alias{atan2}
\title{Trigonometric Functions}
\description{
  These functions give the obvious trigonometric functions.  They
  respectively compute the cosine, sine, tangent, arc-cosine, arc-sine,
  arc-tangent, and the two-argument arc-tangent.
}
\usage{
cos(x)
sin(x)
tan(x)
acos(x)
asin(x)
atan(x)
atan2(y, x)
}
\arguments{
   \item{x, y}{numeric or complex vectors.}
}
\details{
  The arc-tangent of two arguments \code{atan2(y, x)} returns the angle
  between the x-axis and the vector from the origin to \eqn{(x, y)},
  i.e., for positive arguments \code{atan2(y, x) == atan(y/x)}.

  Angles are in radians, not degrees (i.e., a right angle is
  \eqn{\pi/2}).

  All except \code{atan2} are generic functions: methods can be defined
  for them individually or via the \code{\link[base:groupGeneric]{Math}}
  group generic.
}
\section{Complex values}{
   For the inverse trigonometric functions, branch cuts are defined as in
   Abramowitz and Stegun, figure 4.4, page 79.  Continuity on the
   branch cuts is standard.

   For \code{asin()} and \code{acos()}, there are two cuts, both along
   the real axis: \eqn{\left(-\infty, -1\right]}{\(-Inf, -1\]} and
   \eqn{\left[1, \infty\right)}{\[1, Inf\)}.  Functions \code{asin()}
   and \code{acos()} are continuous from above on the interval
   \eqn{\left(-\infty, -1\right]}{\(-Inf, -1\]} and continuous from
   below on \eqn{\left[1, \infty\right)}{\[1, Inf\)}.

   For \code{atan()} there are two cuts, both along the pure imaginary
   axis: \eqn{\left(-\infty i, -1i\right]}{\(-1i*Inf, -1i\]} and
   \eqn{\left[1i, \infty i\right)}{\[1i, 1i*Inf\)}.  It is continuous
   from the left on the interval
   \eqn{\left(-\infty i, -1i\right]}{\(-1i*Inf, -1i\]} and from the
   right on the interval \eqn{\left[1i, \infty i\right)}{\[1i, 1i*Inf\)}.
}
\section{S4 methods}{
  All except \code{atan2} are S4 generic functions: methods can be defined
  for them individually or via the
  \code{\link[methods:S4groupGeneric]{Math}} group generic.
}
\references{
  Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
  \emph{The New S Language}.
  Wadsworth \& Brooks/Cole.

  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}