# Trig {base}

### 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 or complex vectors.

### 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).

All except `atan2`

are internal generic primitive functions: methods can be defined for them individually or via the `Math`

group generic.

### Complex values

For the inverse trigonometric functions, branch cuts are defined as in Abramowitz and Stegun, figure 4.4, page 79.

For `asin`

and `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 direction.

### S4 methods

All except `atan2`

are S4 generic functions: methods can be defined for them individually or via the `Math`

group generic.

### References

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

Documentation reproduced from R 3.0.2. License: GPL-2.