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Math Help - How to approach general solutions?

  1. #1
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    How to approach general solutions?

    If I want to find the general solution of

    sin2\theta + sin4\theta = cos\theta how would I go about doing this?

    What would be a possible method that you could use to solve this question

    Thanks if you can help me
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by db5vry View Post
    If I want to find the general solution of

    sin2\theta + sin4\theta = cos\theta how would I go about doing this?

    What would be a possible method that you could use to solve this question

    Thanks if you can help me
    break things down to sine and cosine. use your trig identities.

    you have: 2 \sin \theta \cos \theta + 2 \sin 2 \theta \cos 2 \theta = \cos \theta

    \Rightarrow 2 \sin \theta \cos \theta + 4 \sin \theta \cos \theta \cos 2 \theta = \cos \theta

    Note that if \cos \theta = 0 we have a solution. So find all the \theta = \frac {n \pi}2 where n is any odd integer is one set of solutions.

    Now assume \cos \theta \ne 0, we can divide by it to get

    2 \sin \theta + 4 \sin \theta \cos 2 \theta = 1

    Now change out \cos 2 \theta to something more convenient and continue


    (instead of this thing about considering whether cosine is zero or not, the standard way would be to bring the cosine on the right to the left, factor it out and set each factor to zero)
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