Hyperbolic Functions
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