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)

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 π/2).

Examples

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