Calc11_1 HypFunc

# Calc11_1 HypFunc - A.P Calculus Hyperbolic Functions Greg...

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Hyperbolic Functions A.P. Calculus: Greg Kelly, Hanford High School, Richland, Washington

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Consider the following two functions: 2 2 x x x x e e e e y y - - - + = = These functions show up frequently enough that they have been given names.
2 2 x x x x e e e e y y - - - + = = The behavior of these functions shows such remarkable parallels to trig functions, that they have been given similar names.

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Hyperbolic Sine: ( 29 sinh 2 x x e e x - - = (pronounced “cinch x”) Hyperbolic Cosine: (pronounced “kosh x”) ( 29 cosh 2 x x e e x - + =
Hyperbolic Tangent: ( 29 ( 29 ( 29 sinh tanh cosh x x x x x e e x x e e - - - = = + “tansh (x)” Hyperbolic Cotangent: ( 29 ( 29 ( 29 cosh coth sinh x x x x x e e x x e e - - + = = - “cotansh (x)” Hyperbolic Secant: ( 29 ( 29 1 2 sech cosh x x x x e e - = = + “sech (x)” Hyperbolic Cosecant: ( 29 ( 29 1 2 csch sinh x x x x e e - = = - “cosech (x)”

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First, an easy one: Now, if we have “trig-like” functions, it follows that we will have “trig-like” identities.
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