Hyperbolic Functions

The Wolfram Language supports hyperbolic functions everywhere in the complex planewith careful attention to branch cutsand 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