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Math Help - mei c3 jun 2006 question- its a toughie

  1. #1
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    mei c3 jun 2006 question- its a toughie

    The question is:

    Show that f(x + π) = (-e^(-1/5)* π)*f(x)

    Background info:
    f(x) = (e^(-1/5)* x)*sin x

    I would really appreciate a walkthrough answer because I've been trying for hours to get their solution with no such luck.

    Thanx
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  2. #2
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    Quote Originally Posted by hopingforhelp View Post
    The question is:

    Show that f(x + π) = (-e^(-1/5)* π)*f(x)

    Background info:
    f(x) = (e^(-1/5)* x)*sin x

    I would really appreciate a walkthrough answer because I've been trying for hours to get their solution with no such luck.

    Thanx
    The only thing I can think to suggest is just to do it!
    Since f(x) is defined as e^{-x/5} \sin (x), f(x+ \pi) = e^{-(x+\pi)/5} \sin (x+\pi). Now you should know that \sin (x+\pi)= -\sin (x) and, by the "laws of exponents", e^{-(x+ \pi)/5}= e^{-x/5- \pi/5}= e^{-x/5}e^{-\pi/5}. Putting those together,
    f(x+\pi)= e^{-x/5}e^{-\pi/5}(-\sin (x))= -e^{-\pi/5}e^{-x/5} \sin (x)= -e^{-\pi/5}f(x).
    Last edited by HallsofIvy; May 27th 2009 at 10:06 AM. Reason: Fixed latex
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  3. #3
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    Thanks so much HallsofIvy, I had no idea that sin(x + π) = -sin x. Do rules like this come under a particular title so that I can search them up on google and learn them for my exam on monday?
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  4. #4
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    Quote Originally Posted by hopingforhelp View Post
    Thanks so much HallsofIvy, I had no idea that sin(x + π) = -sin x. Do rules like this come under a particular title so that I can search them up on google and learn them for my exam on monday?
    sum formula for sine ...

     <br />
\sin(x+\pi) = \sin{x}\cos(\pi) + \cos{x}\sin(\pi) = -\sin{x} + 0 = -sin{x}<br />
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