R: Trigonometric Functions

Trig {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 vector

### 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

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