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Math Help - Solving a trigonometric equation.

  1. #1
    Junior Member
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    Solving a trigonometric equation.

    Hey guys!

    I need help solving the following trigonometric equation:

    7 cos x = 4 - 2 sin^2 x

    I get:

    7 cos x = 4 -2(1-cos^2 x)
    7 cos x = 4 -2 + 2 cos^2 x
    2 cos^2 x - 7 cos x + 2 = 0

    It turns out this doesn't factor very well, and I'm almost sure I made a mistake. None of the problems I'm working on require the quadratic equation so I'm pretty sure that I just solved the equation incorrectly.

    Help?
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  2. #2
    Super Member
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    Quote Originally Posted by JennyFlowers View Post
    Hey guys!

    I need help solving the following trigonometric equation:

    7 cos x = 4 - 2 sin^2 x

    I get:

    7 cos x = 4 -2(1-cos^2 x)
    7 cos x = 4 -2 + 2 cos^2 x
    2 cos^2 x - 7 cos x + 2 = 0

    It turns out this doesn't factor very well, and I'm almost sure I made a mistake. None of the problems I'm working on require the quadratic equation so I'm pretty sure that I just solved the equation incorrectly.

    Help?
    Hey,

    Unfortunately, you do need to use the quadratic equation this time (there is a way to complete the square but that's a mess as well).

    Good luck with that. I've seen the answer and it isn't pretty, so don't get discouraged if things become messy.
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