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Homework Help: Solving an equation for t

  1. Dec 11, 2005 #1
    Hi, can anyone help me to solve this equation for t please.

    1=10*exp((-pi*t)/5)*cos(pi*t)

    Thanks:smile:
     
  2. jcsd
  3. Dec 12, 2005 #2

    Tide

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    HINT: Rewrite the equation as

    [tex]10 \cos \left[ \pi t \left(1 - \frac {i}{5}\right) \right] = 1[/tex]

    Second HINT: Recheck my algebra! ;)
     
  4. Dec 12, 2005 #3

    mathman

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    Note to Tide: Your algebra looks wrong.
     
  5. Dec 14, 2005 #4

    Tide

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    mathman,

    Yes, very! Thanks - but I did give fair warning. :)

    [note to self: do it on paper next time!]
     
  6. Dec 14, 2005 #5

    HallsofIvy

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    Either write cos(pi*t) as
    [tex]\frac{e^{i\pit}+ e^{-i\pit}}{2}[/tex]
    so that the equation becomes
    [tex]1= 10e^{-\frac{\pit}{5}}\(\frac{e^{i\pit}+ e^{-i\pit}}{2}\)= 5\(e^{\pit\(-\frac{1}{5}+ i\)+ e^{\pit\(-\frac{1}{5}- i\)\)[/tex]
    or write exp((-pi*t)/5) as
    [tex]cos(-\frac{\pit}{5})+ i sin(-\frac{\pit}{5})[/tex]
    so the equation becomes
    [tex]1= 10\(cos(\frac{\pit}{5}cos(\pit)- icos(\pit)sin(\frac{pit}{5})\)[/tex]
     
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