Chapter 9.3, Problem 21E

To determine

To find: the rectangular coordinates.

Answer to Problem 21E

The rectangular coordinate is $\left(-\frac{\sqrt{2}}{4},\frac{\sqrt{2}}{4}\right)$ .

Explanation of Solution

Given information: The polar coordinate is $\left(\frac{1}{2},\frac{3\pi }{2}\right)$ .

Calculation:

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

  $\begin{array}{l}\left(r,\theta \right)=\left(\frac{1}{2},\frac{3\pi }{2}\right)\\ x=r\cos \theta \\ \Rightarrow \frac{1}{2}\cos \left(\frac{3\pi }{2}\right)\\ \Rightarrow -\frac{\sqrt{2}}{4}\\ y=r\sin \theta \\ \Rightarrow \frac{1}{2}\sin \left(\frac{3\pi }{2}\right)\\ \Rightarrow \frac{\sqrt{2}}{4}\\ \left(-\frac{\sqrt{2}}{4},\frac{\sqrt{2}}{4}\right)\end{array}$