Trig                  package:base                  R Documentation

_T_r_i_g_o_n_o_m_e_t_r_i_c _F_u_n_c_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

    x, y: numeric or complex vectors.

_D_e_t_a_i_l_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).

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

_C_o_m_p_l_e_x _v_a_l_u_e_s:

     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).

_R_e_f_e_r_e_n_c_e_s:

     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

