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Math Help - Solve the equation of Cos3(theta) = 1/2

  1. #1
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    Solve the equation of Cos3(theta) = 1/2

    Solve the equation of Cos3(theta) = 1/2 , for theta is an element of real numbers, where (theta) is in radius.

    I feel like it's simple but I don't know how :-/
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    Member Goku's Avatar
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    Re: Solve the equation of Cos3(theta) = 1/2

    cos(3\theta) = \frac{1}{2}

    3\theta = cos^{-1}(\frac{1}{2})

    3\theta =60 degrees

    \theta = 20 degrees + 360k where k is any integer.
    Last edited by Goku; June 10th 2012 at 11:58 AM.
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    Re: Solve the equation of Cos3(theta) = 1/2

    Quote Originally Posted by DeeRose View Post
    Solve the equation of Cos3(theta) = 1/2 , for theta is an element of real numbers, where (theta) is in radius.
    Is this supposed to be \cos3\theta=\frac12 or \cos^3\theta = \frac12\mathrm? If the latter, are you looking for an exact solution?
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    Re: Solve the equation of Cos3(theta) = 1/2

    Quote Originally Posted by Goku View Post
    \theta = 20 degrees
    Your procedure is good, but this is only one of infinitely many solutions.
    Thanks from Goku
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    Re: Solve the equation of Cos3(theta) = 1/2

    It's Cos3(theta) ..Not Cos^3(theta) Is Goku's response the right one then?
    Last edited by DeeRose; June 10th 2012 at 12:29 PM.
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    Re: Solve the equation of Cos3(theta) = 1/2

    Quote Originally Posted by DeeRose View Post
    It's Cos3(theta) .. Is Goku's response the right one then?
    Note that cosine is equal to \frac12 for any angle that is coterminal with \frac\pi3 or -\frac\pi3. Thus

    \cos3\theta=\frac12

    \Rightarrow3\theta = 2k\pi\pm\frac\pi3

     = \frac{(6k\pm1)\pi}3

    \Rightarrow\theta = \frac{(6k\pm1)\pi}9

    where k\in\mathbb{Z}.
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    Re: Solve the equation of Cos3(theta) = 1/2

    Thanks alot! :-)
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