A hyperbolic function is related to the trigonometric functions, but instead of being based around the unit circle, they are based on the unit hyperbola: $x^2-y^2=1.$

(none) (none) PoincaresDisc
(none) HyperbolicCosine
HyperbolicSin
NonEuclideanGeometry

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HyperbolicFunction
Function
TrigonometricFunction
UnitCircle
(none) (none) CoDomainOfAFunction
DomainOfAFunction
ImageOfAFunction
Polynomial
RangeOfAFunction
RealNumber