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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The graphs of the polar equations r₁ = cos(29) and r₂ = sin() + 1 are shown below. Find the 4 angles between 0 and 2 for which r₁ = 0, and the angle for which r₂ = 0, please explain every steps clearly. Then find the other six points of intersection (r and 9) of the curves. You should be able to find four values of r and exactly, and find the other two to four decimal places. Hint: r₁ = cos(20) takes on both positive and negative values, while r₂ = sin(9) + 1 takes on only non- negative values. Is &

2. If cos(0) = 0.6 , what are the coordinates of P ? Explain your reasoning. YA