Investigate the equation r = a + b cos (kq) and compare with r = b cos (kq) for various values of k.
Consider the following graphs:
Notice that for equations of the form r = a + b cos (kq), k represents the number of "leaves" or "petals" that the curve has when a and b are equal. These curves are often referred to as "n- leaf roses," with k = n. The same holds true for equations of the form r = b cos (kq) when k is an odd number; when k is even, there are 2k petals.
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