Chapter 9.1, Problem 16AYU

In Problems 11-18, match each point in polar coordinates with either $A,B,C,\text{ or }D$ on the graph.

$\left(2,\frac{11\pi }{6}\right)$

To determine

To find: To match the given point in polar coordinates with either $A$, $B$, $C$, or $D$ on the graph.

Answer to Problem 16AYU

$D$

Explanation of Solution

Given:

$\left(2,\frac{11\pi }{6}\right)$

Formula used:

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

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

Calculation:

$r=2,\theta = \frac{11\text{π}}{6}= \frac{11\times 180°}{6}=330°$

$x=r\text{cos}\theta =2\text{cos}150=2\times \text{cos}\left(360°-30°\right)$

$=2\text{cos}30°$

$=2\times \frac{\sqrt{3}}{2}=\sqrt{3}$

$y=r\text{sin}\theta =2\text{sin}150=-2\times \text{sin}\left(360°-30°\right)$

$=2\left(-\text{sin}30°\right)$

$=-2\times \frac{1}{2}=-1$

$P\left(x,y\right)=(\sqrt{3},-1)$

So it lies in quadrant $Q_4$ and answer is $D$.