The Wolfram Language supports hyperbolic functions everywhere in the complex plane—with careful attention to branch cuts—and provides an extensive web of exact and algebraic transformations, together with efficient arbitrary-precision numerical evaluation.

Sinh  ▪  Cosh  ▪  Tanh  ▪  Csch  ▪  Sech  ▪  Coth

ArcSinh  ▪  ArcCosh  ▪  ArcTanh  ▪  ArcCsch  ▪  ArcSech  ▪  ArcCoth

Gudermannian  ▪  InverseGudermannian

I () — , entered as ii ("imaginary i")

FullSimplify — simplify hyperbolic function expressions

FunctionExpand — reduce to algebraic forms or simpler arguments

TrigToExp, ExpToTrig — convert between hyperbolic and exponential functions

ComplexExpand — expand into real and imaginary parts

TrigExpand  ▪  TrigFactor  ▪  TrigReduce