## Hyperbolic Functions

Hyperbolic functions may be introduced by presenting their similarity to trigonometric functions.

Recalling from trigonometry that any point (x, y) on the unit circle, x

^{2}+ y

^{2}=1, is represented by x = cos t and y = sin t, hyperbolic functions may be used to denote any point (x, y) on the unit hyperbola expressed by x

^{2}− y

^{2}=1. Specifically, the hyperbolic cosine and hyperbolic sine may be used to represent x and y respectively as x = cosh t and y = sinh t.

The hyperbolic functions (e.g., hyperbolic sine, hyperbolic cosine) are defined by:

Similar to trigonometric functions, a fundamental identity exists for hyperbolic functions: