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Math Help - Need help with trigonometric equations please.

  1. #1
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    Need help with trigonometric equations please.

    How would I solve the trig equation 5 cos(2x)=2 ?????????????
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  2. #2
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    Re: Need help with trigonometric equations please.

    \cos 2x = \frac{2}{5}

    What angles within the unit circle have a cosine of 2/5?
    Last edited by richard1234; November 11th 2012 at 09:14 AM.
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  3. #3
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    Re: Need help with trigonometric equations please.

    assuming solutions in the interval 0 < x < 2\pi ...


    0 < x < 2\pi \implies 0 < 2x < 4\pi

    let t = 2x , so 0 < t < 4\pi


    5 \cos{t} = 2

    \cos{t} = \frac{2}{5}

    since \cos{t} > 0 , t is an angle in quads I or IV


    quad I solutions for t , (two) ...

    t = \arccos\left(\frac{2}{5}\right) and t = 2\pi + \arccos\left(\frac{2}{5}\right)

    so x = \frac{1}{2}\arccos\left(\frac{2}{5}\right) and x = \pi + \frac{1}{2}\arccos\left(\frac{2}{5}\right)


    quad IV solutions (two) ...

    t = 2\pi - \arccos\left(\frac{2}{5}\right) and t = 4\pi - \arccos\left(\frac{2}{5}\right)

    so x = \pi - \frac{1}{2}\arccos\left(\frac{2}{5}\right) and x = 2\pi - \frac{1}{2}\arccos\left(\frac{2}{5}\right)
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