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Math Help - Trigonometric equation:

  1. #1
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    Trigonometric equation:

    I am trying to find the solutions for this equation.
    I have worked it twice and keep getting different answers. Can someone show me step by step how to work it?
    sin(2x)-cos(x)=0
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by cmr7 View Post
    I am trying to find the solutions for this equation.
    I have worked it twice and keep getting different answers. Can someone show me step by step how to work it?
    sin(2x)-cos(x)=0
    Recall that \sin\left(2x\right)=2\sin\left(x\right)\cos\left(x  \right)

    Thus, \sin\left(2x\right)-\cos\left(x\right)=0\implies 2\sin\left(x\right)\cos\left(x\right)-\cos\left(x\right)=0\implies \cos\left(x\right)\left[2\sin\left(x\right)-1\right]=0

    Thus, either \cos\left(x\right)=0 or 2\sin\left(x\right)-1=0\implies \sin\left(x\right)=\tfrac{1}{2}

    Can you take it from here? Also, is there a restriction on x [i.e. 0\leq x\leq2\pi]??
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  3. #3
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    I think my brain is just fried and I am over thinking things tonight. No restrictions on x. Thank you for all for your help!
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