Answer
$(-1, -120^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(1, 60^{\circ})$
$(-1, 240^{\circ})$
(c) $(x,y) = (\frac{1}{2},\frac{\sqrt{3}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/f87d71bf-4d84-4b79-b609-6829f16b7d20/result_image/1529302111.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015201Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=0d45c34e8bc4d89574b31feb4914dd840b2a4a57ca68f56e55ab55d312a6d70f)
Work Step by Step
$(-1, -120^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(1, 60^{\circ})$
$(-1, 240^{\circ})$
(c) We can find the rectangular coordinates:
$r = 1$ and $\theta = 60^{\circ}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (1~cos~60^{\circ}, 1~sin~60^{\circ})$
$(x,y) = (\frac{1}{2},\frac{\sqrt{3}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/f87d71bf-4d84-4b79-b609-6829f16b7d20/steps_image/small_1529302111.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015201Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=7ed9d3fc73d767c3c386e0e1933557c4c63b1a29742e27c0d7ffaddc3c35390b)