Calc11_1 HypFunc

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

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Unformatted text preview: Hyperbolic Functions A.P. Calculus: Greg Kelly, Hanford High School, Richland, Washington 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. → 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)” → First, an easy one: Now, if we have “trig-like” functions, it follows that we will have “trig-like” identities....
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Calc11_1 HypFunc - Hyperbolic Functions A.P Calculus Greg...

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