# polar graphs and investigation

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.

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First question: did you try a few examples with specific values of $b$, $n$, $a$? If not, then try them! –  Arturo Magidin Feb 9 '12 at 6:58
If you don't have a graphic software you can use Wolfram Alpha to experiment. –  yohBS Feb 9 '12 at 7:37
Just play around! Don't be afraid... –  Ｊ. Ｍ. Feb 9 '12 at 8:00