Answer
(a) We can see the point plotted on the graph below.
(b) We can write two pairs of polar coordinates for this point:
$(1, 300^{\circ})$
$(-1, 120^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/7cdcaa95-89d9-4d5a-a6c2-49735cd44af0/result_image/1529425090.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013959Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=ffeac81a51b88d6392856f18b6fa53a963f88cd0713087a9480880cf0d5c6009)
Work Step by Step
$(\frac{1}{2}, -\frac{\sqrt{3}}{2})$
(a) We can see the point plotted on the graph below.
(b) $r = \sqrt{(\frac{1}{2})^2+(-\frac{\sqrt{3}}{2})^2} = 1$
We can find the angle $\phi$ below the positive x-axis:
$tan~\phi = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$
$\phi = arctan(\sqrt{3})$
$\phi = 60^{\circ}$
We can write two pairs of polar coordinates for this point:
$(1, 300^{\circ})$
$(-1, 120^{\circ})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/7cdcaa95-89d9-4d5a-a6c2-49735cd44af0/steps_image/small_1529425090.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T013959Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=0e5729c38063ea6b3b94806abe62d64aa35ad786ea61378242272b62af13e07a)