Chapter 9.3, Problem 6E

(a)

(i)

To determine

The polar coordinates $\left(r,\theta \right)$ of the point $\left(3\sqrt{3},3\right)$, where $r>0$ and $0\le \theta <2\pi$.

(ii)

To determine

The polar coordinates $\left(r,\theta \right)$ of the point $\left(3\sqrt{3},3\right)$, where $r<0$ and $0\le \theta <2\pi$.

(b)

(i)

To determine

The polar coordinates $\left(r,\theta \right)$ of the point $\left(1,-2\right)$, where $r>0$ and $0\le \theta <2\pi$.

(ii)

To determine

The polar coordinates $\left(r,\theta \right)$ of the point $\left(1,-2\right)$, where $r<0$ and $0\le \theta <2\pi$.