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Math Help - Finding quadrant for a half angle.

  1. #1
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    Finding quadrant for a half angle.

    I'm given the following problem:

    If cos(x) = \frac{-5}{13} and sin(x) < 0 find cos(\frac{x}{2})

    Since both cos(x) and sin(x) are negative, I know that x lies in quadrant III. But I'm not sure how I can determine what quadrant (\frac{x}{2}) lies in. I know how to solve this problem using the half angle identity, except I'll need to know what sign to put in front of my answer.

    Thanks!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by JennyFlowers View Post
    I'm given the following problem:

    If cos(x) = \frac{-5}{13} and sin(x) < 0 find cos(\frac{x}{2})

    Since both cos(x) and sin(x) are negative, I know that x lies in quadrant III. But I'm not sure how I can determine what quadrant (\frac{x}{2}) lies in. I know how to solve this problem using the half angle identity, except I'll need to know what sign to put in front of my answer.

    Thanks!
    In the third quadrant

    \displaystyle\ {\pi}< x<\frac{3{\pi}}{2}

    \displaystyle\ \frac{{\pi}}{2}< \frac{x}{2}<\frac{3{\pi}}{4}

    The half-angle is in quadrant 2.
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  3. #3
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    Exactly what I needed, thank you!
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