Chapter 12.2, Problem 77E

(a)

To determine

Whether the statement, “The point with Cartesian coordinates $\left(-2,2\right)$ has polar coordinates $\left(2\sqrt{2},\frac{3\pi }{4}\right)\left(2\sqrt{2},\frac{11\pi }{4}\right)\left(2\sqrt{2},-\frac{5\pi }{4}\right)\text{ and }\left(-2\sqrt{2},-\frac{\pi }{4}\right)$” is true or false.

(b)

To determine

Whether the statement, “the graphs of $r\cos \theta =4\text{ and }r\sin \theta =-2$ intersect exactly once” is true or false.

(c)

To determine

Whether the statement, “the graphs of $r=2\text{ and }\theta =\frac{\pi }{4}$ intersect exactly once”, is true or false.

(d)

To determine

Whether the statement, “the point $\left(3,\frac{\pi }{2}\right)$ lies on the graph of $r=3\cos 2\theta$” is true or false.

(e)

To determine

Whether the statement, “the graphs of $r=2\sec \theta \text{ and }r=3\csc \theta$ are lines” is true or false.