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hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

The hyperbolic functions formula:

Hyperbolic sine of x = sinh x = (e^x - e^-x)/2

Hyperbolic cosine of x = cosh x = (e^x + e^-x)/2

Hyperbolic tangent of x = tanh x = (e^x - e^-x)/(e^x + e^-x)

Hyperbolic cotangent of x = coth x = (e^x + e^-x)/(e^x - e^-x)

Hyperbolic secant of x = sech x = 2/(e^x + e^-x)

Hyperbolic cosecant of x = csch x = 2/(e^x - e^-x)