a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine: often expressed as combinations of exponential functions.

British Dictionary definitions for hyperbolic function

hyperbolic function

noun

any of a group of functions of an angle expressed as a relationship between the distances of a point on a hyperbola to the origin and to the coordinate axes. The group includes sinh (hyperbolic sine), cosh (hyperbolic cosine), tanh (hyperbolic tangent), sech (hyperbolic secant), cosech (hyperbolic cosecant), and coth (hyperbolic cotangent)

Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner analogous to the relationship of the trigonometric functions to a circle, including:

The hyperbolic sine, defined by the equation sinh x = 12(ex - e-x).

The hyperbolic cosine, defined by the equation cosh x = 12(ex + e-x).

The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x.

The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.

The hyperbolic secant, defined by the equation sech x = 1/cosh x.

The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.