For the graph of the polar rose ($r=\cos k\theta$), why is it that there 2k petals for even k values while there are only k petals when k is odd? From playing around on Desmos, I understand that when k is odd, the graph overlaps itself after 180 degrees but why is this the case? Why does the graph not also overlap itself when k is even? Thanks in advance for any help.
For the graph of a rose ($r=\cos k\theta$), why d0es are there 2k petals for even values of k while only k petals for odd values of k?
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algebra-precalculus
polar-coordinates
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1Maybe helps http://math.stackexchange.com/questions/626592/prove-that-the-rose-in-the-polar-plane-has-2n-petals-when-n-is-even/626622#626622 – 2017-02-14
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From Wikipedia:
When $k$ is even, the entire graph of the rose will be traced out exactly once when the value of $\theta$ changes from $0$ to $2\pi$. When $k$ is odd, this will happen on the interval between $0$ and $\pi$. (More generally, this will happen on any interval of length $2\pi$ for $k$ even, and $\pi$ for $k$ odd.)
I also request you to see here. Hope it helps.