Chapter 9.1, Problem 44AYU

To determine

To find: Rectangular coordinates for the given polar coordinates.

Answer to Problem 44AYU

$P\left(\frac{5}{2},\frac{-5\sqrt{3}}{2}\right)$

Explanation of Solution

Given:

$r=5,\theta ={300}^{\circ }$

Formula used:

$x=r\text{cos}\theta$

$y=r\text{sin}\theta$

Calculation:

We know that when polar coordinates are given rectangular coordinates are expressed as,

$x=r\text{cos}\theta ,y=r\text{sin}\theta$

$x=5\text{cos}{300}^{\circ },y=5\text{sin}{300}^{\circ }$

$x=5\text{cos}\left({360}^{\circ }-{60}^{\circ }\right),y=5\text{sin}\left({300}^{\circ }-{60}^{\circ }\right)$

$x=5\left(\text{cos}{60}^{\circ }\right),y=5\times (-\text{sin}{60}^{\circ })$

$x=5\times \frac{1}{2},y=5\times - \frac{\sqrt{3}}{2}$

$x=\frac{5}{2},y=\frac{-5\sqrt{3}}{2}$

Hence the rectangular coordinates are $P\left(\frac{5}{2},\frac{-5\sqrt{3}}{2}\right)$.