Explain why or why not Determine whether the

QUESTION:

Determine whether the following statements are true and given an explanation or counterexample.

a. The point with Cartesian coordinates (-2, 2) has polar coordinates \((2\sqrt{2},\ 3\pi/4),\ (2\sqrt{2},\ 11\pi/4),\ (2\sqrt{2},\ -5\pi/4)\), and \((-2\sqrt{2},\ -\pi/4)\).

b. The graphs of \(r \cos \theta =4\) and \(r \sin \theta =-2\) intersect exactly once.

c. The graphs of r = 2 and \(\theta=\pi/4\) intersect exactly once.

d. The point \((3,\ \pi/2)\) lies on the graph of \(r=3 \cos 2\theta\).