Answer
$(3, \frac{5\pi}{3})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(3, -\frac{\pi}{3})$
$(-3, \frac{2\pi}{3})$
(c) $(x,y) = (\frac{3}{2}, -\frac{3\sqrt{3}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/082c0b06-b9e2-407e-9108-19e3997144ed/result_image/1529334491.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020651Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=0ec38b2890ef90d984015690d2e1ba007ad93e3c2e78f4f2f21f1d567d7a0aeb)
Work Step by Step
$(3, \frac{5\pi}{3})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(3, -\frac{\pi}{3})$
$(-3, \frac{2\pi}{3})$
(c) We can find the rectangular coordinates:
$r = 3$ and $\theta = \frac{5\pi}{3}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (3~cos~\frac{5\pi}{3}, 3~sin~\frac{5\pi}{3})$
$(x,y) = (\frac{3}{2}, -\frac{3\sqrt{3}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/082c0b06-b9e2-407e-9108-19e3997144ed/steps_image/small_1529334491.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020651Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2f87dfedb64d954da8dc053e910951ad81cc4a197f5604ee79c67f5bb6b2e0a8)