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Math Help - Solving Quadratic Trigonometric Equations

  1. #1
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    Solving Quadratic Trigonometric Equations

    How do you turn these equations: 2 sin x sec x - 2 sqrt(3) sin x = 0 and

    (2 cos x + sqrt(3)) sin x = 0 into quadratic equation format?
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  2. #2
    Super Member Quacky's Avatar
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    Quote Originally Posted by Devi09 View Post
    How do you turn these equations: 2 sin x sec x - 2 sqrt(3) sin x = 0 and

    (2 cos x + sqrt(3)) sin x = 0 into quadratic equation format?
    Are you sure you want to put them into quadratic equation format? You can solve them by simply factoring.

    You have a common factor of 2Sin(x) in the first equation:

    2 Sin(x)(Sec(x) - sqrt(3))=0

    Either Sin(x)=0
    Or Sec(x)= Sqrt(3)

    Etc... Can you clarify your question?
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  3. #3
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    you have to solve each equation where 0 <= x <= 2pi. So the first one: sin x = 0 or sec = Sqrt(3). So find those in the unit circle and you got your answer?

    as for the second one it's cos x = -Sqrt(3) / 2 or sin x = 0 and once again find those in the unit circle to get your answer I take it?
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  4. #4
    Super Member Quacky's Avatar
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    Quote Originally Posted by Devi09 View Post
    you have to solve each equation where 0 <= x <= 2pi. So the first one: sin x = 0 or sec = Sqrt(3). So find those in the unit circle and you got your answer?

    as for the second one it's cos x = -Sqrt(3) / 2 or sin x = 0 and once again find those in the unit circle to get your answer I take it?
    Yup.
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