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Thread: Graphing Polars

  1. #1
    Member VitaX's Avatar
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    Graphing Polars

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

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

    $\displaystyle \theta = 0 , r=1$

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

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

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

    $\displaystyle \theta = \pi , r=1$

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

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

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

    $\displaystyle \theta = 2\pi , r=1$

    Now I'm supposed to sketch a graph and this is the part I'm confused about. All the examples we did before had $\displaystyle \theta = 0 , r=0$ to start with, so I'm not really sure how to start when $\displaystyle \theta=0 , r=1$. 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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