Chapter 9.3, Problem 22E

To determine

To find: the rectangular coordinates.

Answer to Problem 22E

The rectangular coordinate is $\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)$ .

Explanation of Solution

Given information: The polar coordinate is $\left(-1,-\frac{\pi }{6}\right)$ .

Calculation:

Since $\left(r,\theta \right)$

  $\begin{array}{l}\left(r,\theta \right)=\left(-1,-\frac{\pi }{6}\right)\\ x=r\cos \theta \\ \Rightarrow -1\cos \left(-\frac{\pi }{6}\right)\\ \Rightarrow -\frac{\sqrt{3}}{2}\\ y=r\sin \theta \\ \Rightarrow -1\sin \left(-\frac{\pi }{6}\right)\\ \Rightarrow \frac{1}{2}\\ \left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)\end{array}$