

   Trig {base}                                  R Documentation

   TTrriiggoonnoommeettrriicc FFuunnccttiioonnss

   DDeessccrriippttiioonn::

        These functions give the obvious trigonometric func-
        tions.  They respectively compute the cosine, sine,
        tangent, arc-cosine, arc-sine, arc-tangent, and the
        two-argument arc-tangent.

   UUssaaggee::

        cos(x)
        sin(x)
        tan(x)
        acos(x)
        asin(x)
        atan(x)
        atan2(y, x)

   DDeettaaiillss::

        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).

   SSeeee AAllssoo::

        `Log', `Math'.

   EExxaammpplleess::

        cos(0) == 1
        sin(3*pi/2) == cos(pi)
        x <- rnorm(99)
        all.equal( sin(-x), - sin(x))
        all.equal( cos(-x), cos(x))
        x <- abs(x); y <- abs(rnorm(x))
        all(abs(atan2(y, x) - atan(y/x)) <= .Machine$double.eps)# TRUE
        table(abs(atan2(y, x) - atan(y/x)) / .Machine$double.eps) # depends!

        x <- 1:99/100
        all(Mod(1 - (cos(x) + 1i*sin(x)) / exp(1i*x)) < 1.1 * .Machine$double.eps)
         2* abs(1 - x / acos(cos(x))) / .Machine$double.eps #-- depends ?
        all(abs(1 - x / asin(sin(x))) <= .Machine$double.eps) # TRUE
        all(abs(1 - x / atan(tan(x))) <= .Machine$double.eps) # TRUE

