**DEFINITION OF HYPERBOLIC FUNCTIONS**

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)

**RELATIONSHIPS AMONG HYPERBOLIC FUNCTIONS**

tanh x = sinh x/cosh x

coth x = 1/tanh x = cosh x/sinh x

sech x = 1/cosh x

csch x = 1/sinh x

cosh2x - sinh2x = 1

sech2x + tanh2x = 1

coth2x - csch2x = 1

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