Chapter 9.1, Problem 52AYU

In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point.

$\left(-3.1,{182}^{\circ }\right)$

To determine

To find: Rectangular coordinates for the given polar coordinates.

Answer to Problem 52AYU

$P\left(3.1,0.093\right)$

Explanation of Solution

Given:

$r=-3.1,\theta ={182}^{\circ }$

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

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

$x=-3.1\times \text{cos}\left({182}^{\circ }\right)$,   $y=-3.1\times \text{sin}\left({182}^{\circ }\right)$

$x=-3.1\times \left(-1\right)$,   $y=-3.1\times 0.03$

$x\approx 3.1$,   $y\approx 0.093$

Hence the rectangular coordinates are $P\left(3.1,0.093\right)$.