In graphing the polar equation, (letting A be the angle, being too lazy to put theta every time) r=r(A)=cos(nA), for n a positive integer, one has n petals if n is odd, and 2n petals if n is even. (Letting the domain of A be sufficiently large.) It appears that this is because the petals are repeated more often in the odd cases, but I cannot figure out why. I would be grateful for any clarification. Thanks.