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Math Help - trig equations

  1. #1
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    trig equations

    sin2t=(square root of 2)cost
    [0,360)
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  2. #2
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    Quote Originally Posted by Thelema View Post
    sin2t=(square root of 2)cost
    [0,360)
    Is this your equation,
    sin(2t) = \sqrt{2}~cos(t)

    or is it
    sin^2(t) = \sqrt{2}~cos(t)

    For the first:
    2~sin(t)~cos(t) = \sqrt{2}~cos(t)

    2~sin(t) = \sqrt{2}

    sin(t) = \frac{\sqrt{2}}{2}

    so t = 45, 135.

    For the second:
    sin^2(t) = \sqrt{2}~cos(t)

    1 - cos^2(t) = \sqrt{2}~cos(t)

    cos^2(t) + \sqrt{2}~cos(t) - 1 = 0

    Using the quadratic formula:
    cos(t) = \frac{-\sqrt{2} \pm \sqrt{2 + 4\sqrt{2}}}{2}

    The only valid solution uses the "+" sign, so
    cos(t) = \frac{-\sqrt{2} + \sqrt{2 + 4\sqrt{2}}}{2}

    which, numerically, gives t = 58.826, 301.174.

    -Dan
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