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Math Help - Graphing Polars

  1. #1
    Member VitaX's Avatar
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    Graphing Polars

    Determine the subintervals of the interval 0 \le \theta \le 2\pi where the function r=cos(2\theta) is either increasing or decreasing. Label these intervals I, II, III,...

    To determine pole values set r=0
    0=cos(2\theta) \rightarrow cos^{-1}0=2\theta \rightarrow \theta = \frac{cos^{-1}0}{2}
    \theta= \frac{\pi}{4} , \frac{\pi}{2} , \frac{3\pi}{4} , \pi , \frac{5\pi}{4} , \frac{3\pi}{2} , \frac{7\pi}{4} , 2\pi

    \theta = 0 , r=1

    \theta = \frac{\pi}{4} , r=0

    \theta = \frac{\pi}{2} , r=-1

    \theta = \frac{3\pi}{4} , r=0

    \theta = \pi , r=1

    \theta = \frac{5\pi}{4} , r=0

    \theta = \frac{3\pi}{2} , r=-1

    \theta = \frac{7\pi}{4} , r=0

    \theta = 2\pi , r=1

    Now I'm supposed to sketch a graph and this is the part I'm confused about. All the examples we did before had \theta = 0 , r=0 to start with, so I'm not really sure how to start when \theta=0 , r=1. This part is confusing me. Novice to this stuff.
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  2. #2
    MHF Contributor
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    It would be extremely hard to instruct graphing in polar coordinates via a post. You may want to see your prof or talk to someone who can physical do it with you.
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  3. #3
    Member VitaX's Avatar
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    Quote Originally Posted by dwsmith View Post
    It would be extremely hard to instruct graphing in polar coordinates via a post. You may want to see your prof or talk to someone who can physical do it with you.
    Could you then confirm that what I drew is correct?

    I drew 4 circles. A circle connecting (0,0) and (1,0) ; (0,0) and (-1,0) ; (0,0) and (0,1) ; (0,0) and (0,-1).
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