For what values of on the polar curve r with 0 2p are

Question

Question: 1. (a) Sketch the bounded region inside the lemniscate r² = 4 cos 2θ and outside the circle r = √2.

(b) Compute the area of the region described in part (a)

2. For what values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, are the tangent lines horizontal? Vertical?