# Hyperbolic

##### Hyperbolic Functions

These functions give the obvious hyperbolic functions. They
respectively compute the hyperbolic cosine, sine, tangent, and their
inverses, arc-cosine, arc-sine, arc-tangent (or ‘*area cosine*’,
etc).

- Keywords
- math

##### Usage

```
cosh(x)
sinh(x)
tanh(x)
acosh(x)
asinh(x)
atanh(x)
```

##### Arguments

- x
- a numeric or complex vector

##### Details

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

group generic.

Branch cuts are consistent with the inverse trigonometric functions
`asin`

*et seq*, and agree with those defined in Abramowitz
and Stegun, figure 4.7, page 86. 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 are S4 generic functions: methods can be defined
for them individually or via the
`Math`

group generic.

##### References

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

##### See Also

The trigonometric functions, `cos`

, `sin`

,
`tan`

, and their inverses
`acos`

, `asin`

, `atan`

.

The logistic distribution function `plogis`

is a shifted
version of `tanh()`

for numeric `x`

.

*Documentation reproduced from package base, version 3.3.0, License: Part of R 3.3.0*