In polar coordinates dealing with the rose figures, whats the relationship between even & odd numbers?

the rose polar coordinates how come when k is even there are 2k petals but when k is odd its that exact amount of petals? why is that relationship different for odd and even values of k?
In polar coordinates dealing with the rose figures, whats the relationship between even %26amp; odd numbers?
actually what appears to be true is not true.....in the interval [0,2π] both sin (even Θ) and sin (odd Θ) have double the number of leaves. You just don't see the "double" number with the " odd Θ " since the leaves lie on top of each other...try r = sin 3 Θ on [0, π] vs on [π, 2 π] and then sin 2 Θ on each of those. When you compare two graphs you should use the same domains.
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