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Cos(nt) = 3sin(2nt) + cos(2nt)

  1. Sep 2, 2010 #1
    Picked up a question and decided to try my hands on it.

    I got to this point where I'm to find 't' and I got stuck. Anyone wants to help?

    cos(nt) = 3sin(2nt) + cos(2nt)
    where n is a constant.

    I tried making nt=x and use double angles but still not getting through.

    Thanks
     
  2. jcsd
  3. Sep 3, 2010 #2
    Re: Trigonometry.

    Well... I posted to here wrong.. excuse me
     
    Last edited: Sep 3, 2010
  4. Sep 3, 2010 #3
    Re: Trigonometry.

    Try using Euler's formulas

    [tex]\cos x=(e^{ix}+e^{-ix})/2[/tex]

    [tex]\sin x=(e^{ix}-e^{-ix})/2i[/tex]

    Your equation will become a second order polynomial in [tex]e^{int}[/tex] which should be easy to solve.
     
  5. Sep 3, 2010 #4

    CompuChip

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    Science Advisor
    Homework Helper

    Re: Trigonometry.

    I have also found a slightly more elaborate way, which I will post if you're interested (Petr's idea is probably more useful though).
     
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