What is "n" when r=sin(nθ) graphs 14 equally spaced loops?
This is an extra credit for my trigonometry class. I have been working on it quite a bit, but in case I can't figure it out before next class, I want to see if my professor give me partial credit for finding the answer on the internet.
If it helps, he said that if we do find the answer, it won't be by punching in all sorts of values for "n" on a calculator. He was very specific that, if we could even figure it out, we would slap our forehead wondering why we didn't think of that before. Any ideas?
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14 loops in 1-up 1-down pairs are 7 complete cycles of the sine wave, but over what horizontal distance? If you get 7 cycles over a distance of 2π, then the period is 2π/7 and so n = 2π / (2π/7) = 7. In general, if the period is b, then n is 2π/b.
Earlier answer was before coffee. Sorry.
n = 3.5
http://en.wikipedia.org/wiki/Rose_%28mathematics%2...
http://www.wolframalpha.com/input/?i=polar+plot+r+...