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.

ReferenceReference

Sinh ▪ Cosh ▪ Tanh ▪ Csch ▪ Sech ▪ Coth

ArcSinh ▪ ArcCosh ▪ ArcTanh ▪ ArcCsch ▪ ArcSech ▪ ArcCoth

Gudermannian ▪ InverseGudermannian

I () , entered as EsciiEsc ("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

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