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Math Help - Compound trig problem and general solutions

  1. #1
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    Compound trig problem and general solutions

    Hi - Needs some pointers on this question as can't find any examples like it in any books.

    Find the general solutions to:

     \cos \left(7\theta \right) = \cos \left( 9\theta - \frac \pi{7} \right )

    Not really sure where to start with this at all! I know the general solution formulas but need a push in the right direction. Do I use the sum and difference identities, or compound identities to get to the double angle ones.?? really not sure so your help would be great.

    Thanks, Felix
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Compound trig problem and general solutions

    In general, if \cos(x)=\cos(a) then all the solutions are:
    x=\pm a + 2k\pi
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  3. #3
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    Re: Compound trig problem and general solutions

    I know the general solution but how do I manipuate the equation to give me a principle value I can then work with?
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  4. #4
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    Re: Compound trig problem and general solutions

    Quote Originally Posted by FelixHelix View Post
    I know the general solution but how do I manipuate the equation to give me a principle value I can then work with?
    The principal value is the solution to 7\theta = 9\theta - \dfrac{\pi}{7}
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  5. #5
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    Re: Compound trig problem and general solutions

    I see. So after manipulating this I get:

     \theta = \pm \frac\pi{14} + n\pi

     \left(n \in \mathbb{Z} \right)

    Could you confirm this?
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  6. #6
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    Re: Compound trig problem and general solutions

    Quote Originally Posted by FelixHelix View Post
    I see. So after manipulating this I get:

     \theta = \pm \frac\pi{14} + n\pi

     \left(n \in \mathbb{Z} \right)

    Could you confirm this?
    Yep, you can also check in the original equation
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