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I am new to polar graphs and I am trying to investigate some certain cases:

  1. What happens when you change the $b$ value to different positive integers in polar equations of the forms: $r=b\cos(\theta)$ and $r=b\sin(\theta)$?

  2. What happens when you keep $b$ constant, but change the $n$ value to different positive integers in polar equations of the forms: $r=b\cos(n\theta)$, $r=b\sin(n\theta)$?

  3. What happens when you keep $b$ and $n$ constant, but change the $a$ value to different integers in polar equations of the forms: $r=a+b\cos(n\theta)$, $r=a+b\sin( n \theta)$?

Thanks.

  • 3
    First question: did you try a few examples with specific values of $b$, $n$, $a$? If not, then try them!2012-02-09
  • 1
    If you don't have a graphic software you can use [Wolfram Alpha](http://www.wolframalpha.com/input/?i=polarplot+r%3D++cos[2+theta]) to experiment.2012-02-09
  • 2
    Just play around! Don't be afraid...2012-02-09

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