Course Number Section 5.8 Hyperbolic Functions Instructor Objective: In this lesson you learned about the properties of Date hyperbolic functions and how to find derivatives and antiderivatives of hyperbolic functions. (Pages Hyperbolic Functions What you should learn How to develop Complete the following definitions of the hyperbolic functions. properties of hyperbolic functions tanh = (sinh / (cosh . x x) x) csch = 1 / (sinh 0 . x x), x sech = 1 / (cosh . x x) coth = 1 / (tanh 0 . x x), x Complete the following hyperbolic identities. cosh2 sinh2 = 1 . x x tanh2 sech2 = 1 . + x x coth2 csch2 = 1 . x x + cosh 2 x = sinh2 . x 2 1 cosh 2 + = cosh2 . 2 x x sinh cosh = sinh 2x . x x cosh2 sinh2 = cosh 2x . x + x sinh (x + sinh cosh + cosh sinh . y)= x y x y sinh (x sinh cosh cosh sinh . y)= x y x y cosh (x + cosh cosh + sinh sinh . y)= x y x y cosh (x cosh cosh sinh sinh . y)= x y x y
Section 5.8 Hyperbolic Functions Objective: In this lesson you learned about the properties of hyperbolic functions and how to find derivatives and antiderivatives of hyperbolic functions. Hyperbolic Functions (Pages Complete the following definitions of the hyperbolic functions. Course Number Instructor Date What you should learn How to develop properties of hyperbolic functions tanh x = (sinh x) / (cosh x) . csch x = 1 / (sinh x), x 0 . sech x = 1 / (cosh x) . coth x = 1 / (tanh x), x 0 . Complete the following hyperbolic identities. cosh2 x sinh2 x = 1 . tanh2 x + sech2 x = 1 . coth2 x csch2 x = 1 . + cosh 2 x 2 = sinh2 x . 1 + cosh 2 x 2 = cosh2 x . sinh x cosh x = sinh 2x . cosh2 x + sinh2 x = cosh 2x . sinh (x + y)= sinh x cosh y + cosh x sinh y . sinh (x y)= sinh x cosh y cosh x sinh y . cosh (x + y)= cosh x cosh y + sinh x sinh y . cosh (x y)= cosh x cosh y sinh x sinh y .
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