An Etymological Dictionary of Astronomy and Astrophysics

Any of the six functions sinh, cosh, tanh, coth, csch, and sech that are related to the → hyperbola in the same way the → trigonometric functions relate to the → circle. Many of the formulae satisfied by the hyperbolic functions are similar to corresponding formulae for the trigonometric functions,
except for + and - signs. For example: cosh²x - sinh²x = 1. See also: → hyperbolic cosine, → hyperbolic sine. Hyperbolic functions were first introduced by the Swiss mathematician Johann Heinrich Lambert (1728-1777).

See also: → hyperbolic; → function.