Question

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.

x = 4 sin²(t), y = 4 cos²(t), 0 ≤ t ≤ 2π

What is the length of the curve?

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Consider the function r = 2 cos(θ) + sin(2θ).

By looking at the Cartesian graph, where is r ≤ 0? (For 0 ≤ θ ≤ 2π. Enter your answer using interval notation.)

How many values of θ for 0 ≤ θ ≤ 2π satisfy r = 1?