PP 7.7 - Hyperbolic Functions Definition The hyperbolic...

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Hyperbolic Functions
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Definition sinh(x) cosh(x) coth(x) cosh(x) sinh(x) tanh(x) cosh(x) 1 sech(x) 2 e e cosh(x) sinh(x) 1 csch(x) 2 e e sinh(x) x x x x = = = + = = - = - - The hyperbolic functions are defined in terms of the exponential function. They are analogous to the trigonometric functions.
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Graphs y = sinh(x) y = cosh(x)
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Graphs y = tanh(x) y = coth(x)
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Graphs y = csch(x) y = sech(x)
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Examples Find the value of each expression. ) 2 sinh( . 1 2 4 2 2 2 1 2 e e e e - = - = - )) 5 cosh(ln( . 2 10 24 2 5 2 5 1 ) 5 ln( ) 5 ln( = - = + = - e e cosh(x). find , ) sinh( If . 3 4 3 = x 4 5 16 25 2 16 9 2 ) cosh( ) ( cosh 1 cosh = = = - x x (x)
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Hyperbolic Identities ) sinh( ) sinh( ) cosh( ) cosh( ) cosh( ) sinh( ) cosh( ) cosh( ) sinh( ) sinh( ) ( sec ) ( tanh 1 1 ) ( sinh ) ( cosh ) cosh( ) cosh( ) sinh( ) sinh( 2 2 2 2 y x y x y x y x y x y x x h x x x x x x x + = + + = + = - = - = - - = -
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Proof of Some Identities ) sinh( 2 2 2 ) sinh( ) ( x e e e e e e x x x x x x x - = - - = - = - = - - - - - - ( 29 [ ] 1
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PP 7.7 - Hyperbolic Functions Definition The hyperbolic...

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