Trig                  package:base                  R Documentation

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:

    x, y: numeric or complex vectors.

Details:

     The arc-tangent of two arguments 'atan2(y, x)' returns the angle
     between the x-axis and the vector from the origin to (x, y), i.e.,
     for positive arguments 'atan2(y, x) == atan(y/x)'.

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

     All except 'atan2' are generic functions: methods can be defined
     for them individually or via the 'Math' group generic.

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 'asin()' and 'acos()', there are two cuts, both along the real
     axis: (-Inf, -1] and [1, Inf).  Functions 'asin()' and 'acos()'
     are continuous from above on the interval (-Inf, -1] and
     continuous from below on [1, Inf).

     For 'atan()' there are two cuts, both along the pure imaginary
     axis: (-1i*Inf, -1i] and [1i, 1i*Inf).  It is continuous from the
     left on the interval (-1i*Inf, -1i] and from the right on the
     interval [1i, 1i*Inf).

S4 methods:

     All except 'atan2' are S4 generic functions: methods can be
     defined for them individually or via the 'Math' group generic.

References:

     Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) _The New S
     Language_. Wadsworth & Brooks/Cole.

     Abramowitz, M. and Stegun, I. A. (1972). _Handbook of Mathematical
     Functions,_ New York: Dover.
      Chapter 4. Elementary Transcendental Functions: Logarithmic,
     Exponential, Circular and Hyperbolic Functions

