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d0minicz

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Question

« on: August 06, 2010, 07:35:48 pm »

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Express the following functions in terms of hyperbolic sines and/or hyperbolic cosines of multiples of x.
a) $sinh^{5}(x)$
b) $cosh^{6}(x)$

thanks

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brightsky

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Re: Question

« Reply #1 on: August 06, 2010, 08:31:58 pm »

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$\sinh^5(x)$

$= \left(\frac{e^{x} - e^{-x}}{2}\right)^5$

$= \frac{e^{-5x} + 5e^{-3x} - 10e^{-x} + 10e^{x} - 5e^{3x} + e^{5x}}{32}$

$= \frac{1}{16}\left(\frac{e^{-5x} + e^{5x}}{2} - \frac{5e^{3x} - 5e^{-3x}}{2} + \frac{10e^{x} - 10e^{-x}}{2}\right)$

$= \frac{1}{16} (\cosh(5x) - 5\sinh(3x) + 10\sinh(x))$

Similar process for b).

« Last Edit: August 06, 2010, 08:36:22 pm by brightsky »

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d0minicz

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Re: Question

« Reply #2 on: August 06, 2010, 09:21:52 pm »

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ahh thanks
howd you manage the expansion? binomial expansion?

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jimmy999

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Re: Question

« Reply #3 on: August 06, 2010, 09:32:46 pm »

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Binomial would be the best way. Other methods would be longer

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