HyperbolicFcns - Hyperbolic Functions The Hyperbolic Sine...

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Hyperbolic Functions
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The Hyperbolic Sine, Hyperbolic Cosine & Hyperbolic Tangent x x x x x x x x e e e e x x x e e x e e x - - - - + - = = - = + = cosh sinh tanh 2 sinh 2 cosh
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The Inverse Hyperbolic Cotangent, Hyperbolic Secant & Hyperbolic Cosecant x x x x x x x x e e x hx e e x hx e e e e x x x x - - - - - = = + = = - + = = = 2 sinh 1 csc 2 cosh 1 sec sinh cosh tanh 1 coth
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Values ). 2 csc( . 4 ) 3 coth(ln . 3 ) 0 tanh( . 2 ) 2 cosh(ln . 1 : following the of each exactly Find
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1 2 1 2 1 2 2 ) 2 csc( 3 4 5 8 10 3 1 3 3 1 3 ) 3 coth(ln 3 0 1 1 1 1 0 tanh 2 4 5 2 2 1 2 2 ) 2 cosh(ln . 1 4 2 2 4 2 2 2 2 3 ln 3 ln 3 ln 3 ln 0 0 0 0 2 ln 2 ln - = - = - = - = = = - + = - + = = + - = + - = = + = + = - - - - - - e e e e e e e e e e e e e e e e e e Solution
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Remember Logarithmic Identities ( Calculus I ) x a I x a = log . 7 . 3 . 2 7 5 . 1 : 7 ln ln 7 log 5 = = = e x e Examples x
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Logarithmic Identities II n a a x x n II log log . = x x x Examples 1 1 25 1 2 2 3 2 3 3 ln ln ln . 4 ln 5 ln 5 ln 2 . 3 25 ln 5 ln 5 ln 2 . 2 25 log 5 log 5 log 2 . 1 : = = - = = - = = = = - -
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Identities x h x h x h x x x x x x x x x x x x x 2 2 2 2 2 2 2 2 2 2 csc 1 coth ) 7 ( 1 sec tanh ) 6 ( 2 1 2 cosh sinh ) 5 ( 2 1 2 cosh cosh ) 4 ( sinh cosh 2 cosh ) 3 ( cosh sinh 2 2
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