Graph the curves having the following polar equations. (a) r² = sin(20). Explain how the curve relates to the lemniscate of Bernoulli. (b) r = sin 30 and r = sin(40). Explain why the number of "petals" in the two curves are so different. (c) r = 1 + cos ("cardioid") and r= 1 + 2 cos() ("limaçon") Discuss the similar- ities and differences of the curves. For what values of 0 does the limaçon intersect itself?

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