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Thread: 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 $\displaystyle \displaystyle \begin{align*} \sin{(2x)} = \sqrt{3}\,\cos{(x)} \end{align*}$?
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    Re: Need to find all values of X in the interval [0, 2pi]

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