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Math Help - Solve the equation for exact solutions in the interval )[0°,360°)

  1. #1
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    Solve the equation for exact solutions in the interval )[0°,360°)

    use an algebraic method.
    this is pretty simple but i can't figure it out.
    i just need help working out the question.

    the question is: 2sinθ-1=cscθ
    the answers are 90°, 210°, 330°.

    2sinθ-1= 1/sinθ
    (2sinθ-1)*sinθ= (1/sinθ)*sinθ
    2sin^2θ-sinθ= 1
    sinθ(2sinθ-1)= 1

    sinθ=1
    θ=90°

    2siθ°-1=1
    2sinθ=2
    sinθ=1
    .... i can't get the answers 210° and 330°, which would make sinθ= -1/2
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  2. #2
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    sorry about the extra ), that was a typo.
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  3. #3
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    Quote Originally Posted by somanyquestions View Post

    2sinθ-1= 1/sinθ
    (2sinθ-1)*sinθ= (1/sinθ)*sinθ
    2sin^2θ-sinθ= 1
    sinθ(2sinθ-1)= 1
    from here,

    \sin \theta (2\sin\theta -1)= 1

    2\sin^2 \theta -\sin\theta = 1

    2\sin^2 \theta -\sin\theta - 1=0

    Now make a =\sin \theta giving

    2a^2 -a  - 1=0

    Solve this quadratic.
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