ATAR Notes: Forum

Uni Stuff => Science => Faculties => Mathematics => Topic started by: d0minicz on August 06, 2010, 07:35:48 pm

Title: Question
Post by: d0minicz on August 06, 2010, 07:35:48 pm: 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
Title: Re: Question
Post by: brightsky on August 06, 2010, 08:31:58 pm: $\sinh^5(x)$

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

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

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

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

Similar process for b).
Title: Re: Question
Post by: d0minicz on August 06, 2010, 09:21:52 pm: ahh thanks
howd you manage the expansion? binomial expansion?
Title: Re: Question
Post by: jimmy999 on August 06, 2010, 09:32:46 pm: Binomial would be the best way. Other methods would be longer