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.
cos(x) sin(x) tan(x) acos(x) asin(x) atan(x) atan2(y, x)
- x, y
- numeric or complex vectors.
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 $\pi/2$).
For the inverse trigonometric functions, branch cuts are defined as in
Abramowitz and Stegun, figure 4.4, page 79. For
acos, there are two cuts, both along
the real axis: $(-Inf, -1]$ and
$[1, Inf)$. For
atan there are two cuts, both along the pure imaginary
axis: $(-1i*Inf, -1i]$ and
$[1i, 1i*Inf)$. The behaviour actually on the cuts follows the C99 standard which
requires continuity coming round the endpoint in a counter-clockwise
atan2 are S4 generic functions: methods can be defined
for them individually or via the
Math group generic.
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