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Math Help - Trigonometric equation

  1. #1
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    Trigonometric equation

    Hello,

    I have made attempts to find the solutions to th eeqution 2 sin x + csc x = 0 on the interval [0, 2pi). So, in my disconcertion, I flipped to the answer key and found the steps to finding solution. The steps are as follows:

    2 sin x + csc X = 0 ---> 2 sin x + 1/sin x = 0

    2 sin x + 1 = 0

    What did they do to procure step three? Where did the denominator go? On that step I had gotten (2 sin x + 1)/sin x.

    Thank you
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  2. #2
    Super Member Quacky's Avatar
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    Re: Trigonometric equation

    Your intermediate step is fine. But the only way a fraction can be equal to 0 is if the numerator is 0.
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  3. #3
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    Re: Trigonometric equation

    I disagree w/ the "answer" key ...

    2\sin{x} + \frac{1}{\sin{x}} = 0

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

    this equation has no real solution.
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  4. #4
    Super Member Quacky's Avatar
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    Re: Trigonometric equation

    Whoops, I should have spent more time checking.
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