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Math Help - find all solutions for sec^2 (theta) - 4 = 0

  1. #1
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    find all solutions for sec^2 (theta) - 4 = 0

    okay so I get that I factor it out with difference of two squares

    (sec theta - 2)(sec theta +2)=0
    so
    sec theta = 2
    sec theta= -2

    therefore
    cos theta = 1/2 = pi/3 which gives me the solutions: (pi/3 + 2pi N) and (2pi/3 + 2pi N)

    what I don't understand is this...since cos theta also = -1/2 shouldn't the solutions also include

    (4pi/3+2pi N) and (5pi/3 + 2pi N)?
    Last edited by dangsos; December 1st 2011 at 05:46 PM.
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  2. #2
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    Re: find all solutions for sec^2 (theta) - 4 = 0

    \cos{t} = \frac{1}{2} at t = \frac{\pi}{3} and t = \frac{5\pi}{3}

    \cos{t} = -\frac{1}{2} at t = \frac{2\pi}{3} and t = \frac{4\pi}{3}
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