Chapter 10.2, Problem 6ES

In each part, find polar coordinates satisfying the stated conditions for the point whose rectangular coordinates are $\left(-\sqrt{3},1\right).$

$\begin{array}{l}\left(\text{a}\right)r\ge 0\text{ and 0}\le \theta \text{<2}\pi \\ \left(\text{b}\right)r\le 0\text{ and 0}\le \theta \text{<2}\pi \\ \left(\text{c}\right)r\ge 0\text{ and }-2\pi \text{<}\theta \le 0\\ \left(\text{d}\right)r\le 0\text{ and }-\pi <\theta \le \pi \end{array}$