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Math Help - Trig Equations

  1. #1
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    Oct 2008
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    Trig Equations

    Solve for 0 less than or equal to x less than or equal to 360.

    a) cos2x = tan2x

    b) cos3x + cosx = 0

    Many thanks in advance.
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  2. #2
    Super Member
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    Jun 2008
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    a) \cos{2x} = \tan{2x}

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

    Multiply both sides by \cos{2x}

    \cos^2{2x} = \sin{2x}

    Rearrange and use the Pythagorean identity sin^2(x) + cos^2(x) = 1:

    0 = \sin^2{2x} + \sin{2x} - 1

    Use the quadratic formula:

    \sin{2x} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
    `
    Although it's kind of long, but you have to use the identities:
    \cos{(A\pm B)} = \cos{A}\cos{B} \mp \sin{A}\sin{B}

    \sin{2x} = 2\sin{x}\cos{x}

    Keep expanding the cosines/sines until you get everything in the same angle.
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  3. #3
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    Chop Suey, how can cos2x equal tan2x? Aren't they two different things?
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