Points at which the graphs of r = f() and r = g() intersect must be determined

Points at which the graphs of r = f(θ) and r = g(θ) intersect must be determined carefully. Solving f(θ) = g(θ) identifies some—but perhaps not all—intersection points. The reason is that the curves may pass through the same point for different values of θ. Use analytical methods and a graphing utility to find all the intersection points of the following curves.

r² = cos 2θ and r² = sin 2θ