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 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 generic 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. Continuity on the
branch cuts is standard.

For `asin()`

and `acos()`

, there are two cuts, both along
the real axis: *(-Inf, -1]* and
*[1, Inf)*. Functions `asin()`

and `acos()`

are continuous from above on the interval
*(-Inf, -1]* and continuous from
below on *[1, Inf)*.

For `atan()`

there are two cuts, both along the pure imaginary
axis: *(-1i*Inf, -1i]* and
*[1i, 1i*Inf)*. It is continuous
from the left on the interval
*(-1i*Inf, -1i]* and from the
right on the interval *[1i, 1i*Inf)*.

### 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

[Package

*base* version 2.5.0

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