base (version 3.2.1)

Hyperbolic: Hyperbolic Functions

Description

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).

Usage

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

Arguments

x

a numeric or complex vector

S4 methods

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

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.

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.