This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Hyperbolic Functions
Mathematica 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
I () , entered as Esc ii Esc ("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