(a) Plot r() = 1 cos(10) for 0 2. (b) Compute the area...

(a) Plot r(θ) = 1 − cos(10θ) for 0 ≤ θ ≤ 2π.
(b) Compute the area enclosed inside the ten petals of the graph of r(θ).
(c) Explain why, for a positive integer n and 0 ≤ θ ≤ 2π, r_n(θ) = 1 − cos(nθ) traces out an n-petal flower inscribed in a circle of radius 2 centered at the origin.

(d) Show that the area enclosed inside the n petals of the graph of rn(θ) is independent of n and equals 3/8 A, where A is the area of the circle of radius 2.