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Homework Help: Help Solving for X (Easy I think)

  1. Oct 8, 2013 #1
    sinxcosx+[itex]\frac{1}{2}[/itex]sin2x = 0.0392

    I can't figure out how to solve for x on this one...

    I tried sin2x = cosxsinx but still can't get anywhere.
  2. jcsd
  3. Oct 8, 2013 #2


    Staff: Mentor

    In future posts, don't discard the homework template.

    For this problem, I don't see an easy analytic solution that would allow writing the left-hand side in terms of either sin(x) or cos(x). Having said that, there are lots of numerical methods that would give an approximate solution.
  4. Oct 8, 2013 #3


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    Science Advisor
    Homework Helper
    Gold Member

    Hopefully you mean ##\sin(2x) = 2\sin x\cos x##. Were you given the right side as .0392 or is that a decimal approximation to what you were actually given? Anyway, calling that constant ##k##, you can write your equation as$$
    \frac{\sin(2x)}{2} + \frac 1 2(\frac{1-\cos(2x)}{2})=k$$ $$
    2\sin(2x) + 1 - \cos(2x) = 4k$$ $$
    \frac 2 {\sqrt 5}\sin(2x) - \frac 1 {\sqrt 5}\cos(2x) = \frac {4k-1}{\sqrt 5}$$
    You can write that as a single trig function of ##2x## plus a phase angle using an addition formula. You will at least symbolically be able to solve for ##x## although you may need a calculator to evaluate it exactly.
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