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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 triglike functions, it follows that we will have triglike identities....
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 Spring '08
 Smith
 Hyperbolic Functions

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