Answer
(a) We can see the point plotted on the graph below.
(b) We can write two pairs of polar coordinates for this point:
$(1, 210^{\circ})$
$(-1, 30^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ffb33437-8539-4617-ba12-7b7d04d64fb7/result_image/1529399966.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020425Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=b36114255aea35e3eaf2de0c10c482144607967dbce7c8fe64b2580114205f42)
Work Step by Step
$(\frac{-\sqrt{3}}{2}, -\frac{1}{2})$
(a) We can see the point plotted on the graph below.
(b) $r = \sqrt{(\frac{-\sqrt{3}}{{2}})^2+(-\frac{1}{2})^2} = 1$
We can find the angle $\phi$ below the negative x-axis:
$tan~\phi = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$
$\phi = arctan(\frac{1}{\sqrt{3}})$
$\phi = 30^{\circ}$
We can write two pairs of polar coordinates for this point:
$(1, 210^{\circ})$
$(-1, 30^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ffb33437-8539-4617-ba12-7b7d04d64fb7/steps_image/small_1529399966.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020425Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1594e35cad277251c0136c855987beadfcfeb92b87c816fb78b9c9afcad3ba0a)