The hyperbolic functions sinh z, cosh z, tanh z, csch z, sech z, coth z (hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and hyperbolic cotangent) are analogs of the circular functions, defined by removing is appearing in the complex exponentials. For example, cos z = 1/2(e^(i z) + e^(-i z)), so cosh z = 1/2(e^z + e^(-z)). Note that alternate notations are sometimes used, as summarized in the following table.

double-angle formulas | Fibonacci hyperbolic functions | generalized hyperbolic functions | half-angle formulas | hyperbolic cosecant | hyperbolic cosine | hyperbolic cotangent | hyperbolic secant | hyperbolic sine | hyperbolic tangent | inverse hyperbolic functions | Osborn's rule