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Math Help - find solutions in eqautions in interval

  1. #1
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    find solutions in eqautions in interval

     <br />
\cos\theta = -\frac{1}{2}, 0<= \theta < 2\pi<br />

    how do we find all solutions in that interval given. thanks
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  2. #2
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    Quote Originally Posted by jvignacio View Post
     <br />
\cos\theta = -\frac{1}{2}, 0<= \theta < 2\pi<br />

    how do we find all solutions in that interval given. thanks
    Hello JV,

    \cos \theta=-\frac{1}{2}

    \cos 60=\frac{1}{2}

    Cosine is negative in QII and QIII.

    Reference angle in QII = 180 - 60 = 120 degrees or \frac{2\pi}{3} radians

    Reference angle in QIII = 180 + 60 = 240 degrees or \frac{4\pi}{3} radians

    In radians:
    \theta=\left\{\frac{2\pi}{3}, \frac{4\pi}{3}\right\} over the interval 0 \leq \theta \leq 2\pi

    In degrees:

    \theta=\left\{120^{\circ}, 240^{\circ}\right\} over the interval 0^{\circ} \leq \theta \leq 360^{\circ}
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