Chapter 9.3, Problem 24E

To determine

To find: the rectangular coordinates.

Answer to Problem 24E

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

Explanation of Solution

Given information: The polar coordinate is $\left(4,{210}^{\circ }\right)$ .

Calculation:

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

  $\begin{array}{l}\left(r,\theta \right)=\left(4,{210}^{\circ }\right)\\ x=r\cos \theta \\ \Rightarrow 4\cos \left(\frac{7\pi }{6}\right)\\ \Rightarrow -2\sqrt{3}\\ y=r\sin \theta \\ \Rightarrow 4\sin \left(\frac{7\pi }{6}\right)\\ \Rightarrow -2\\ \left(-2\sqrt{3},2\right)\end{array}$