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Math Help - Need to find all values of X in the interval [0, 2pi]

  1. #1
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    Need to find all values of X in the interval [0, 2pi]

    Find all values of X in the interval [0,2pi]


    sin 2x =
    3
    cos x
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  2. #2
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    Re: Need to find all values of X in the interval [0, 2pi]

    I can't read your equation. Is it \displaystyle \begin{align*} \sin{(2x)} = \sqrt{3}\,\cos{(x)} \end{align*}?
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    Re: Need to find all values of X in the interval [0, 2pi]

    Assuming that it is sin(2x)= \sqrt{3}cos(x), use a trig identity: sin(2x)= 2sin(x)cos(x)= \sqrt{3}cos(x) one solution is cos(x)= 0 which gives x= \pi/2. If cos(x) is NOT 0, we can divide both sides to get 2sin(x)= \sqrt{3} so that sin(x)= \frac{\sqrt{3}}{2}. Can you solve that?
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