Calc11_1 HypFunc - Hyperbolic Functions Greg Kelly, Hanford...

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Unformatted text preview: Hyperbolic Functions Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2005 Scottys Castle, Death Valley, CA 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 Greg Kelly, Hanford...

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