# Trig

##### Trigonometric Functions

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.

- Keywords
- math

##### 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 $\pi/2$).

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 package base, version 3.0.3, License: Part of R 3.0.3*