Find the maximum value of |r| and any zeros of r. (Assume 0 ≤ θ < 2π. Enter any zeros as a comma-separated list.)

Question

r = 19 - 19sinθ

Answer 1

this is just a cardioid. maximum distance is 18 at θ=3π/2
to check,
r' = 19cosθ
r'=0 at θ = π/2, 3π/2
r is minimum at π/2, max at 3π/2