Calculus question

Question

Consider the polar curve r = 1 + a cos θ for 0 ≤ θ ≤ 2π. How many times does the curve intersect with the origin?

Answer 1

r = 1 + a cos θ for 0 ≤ θ ≤ 2π.

Consider how many times Cos θ = -1 for 0 ≤ θ ≤ 2π.

Once when θ = π.