Answer
$(5, -60^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(5, 300^{\circ})$
$(-5, 120^{\circ})$
(c) $(x,y) = (\frac{5}{2},-\frac{5\sqrt{3}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/843ae764-b71a-4287-8f29-9dddac6eb43c/result_image/1529298264.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015323Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=8b691df38c853658aeb7eee605a77cfaf38d8e4b4cd03b5c9e519878625e4221)
Work Step by Step
$(5, -60^{\circ})$
(a) We can see the point plotted on the graph below.
(b) We can write two other pairs of polar coordinates for this point:
$(5, 300^{\circ})$
$(-5, 120^{\circ})$
(c) We can find the rectangular coordinates:
$r = 5$ and $\theta = 300^{\circ}$
$(x,y) = (r~cos~\theta, r~sin~\theta)$
$(x,y) = (5~cos~300^{\circ}, 5~sin~300^{\circ})$
$(x,y) = (\frac{5}{2},-\frac{5\sqrt{3}}{2})$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/843ae764-b71a-4287-8f29-9dddac6eb43c/steps_image/small_1529298264.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015323Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=d9a3b230b269223bcd877b11bf93107b2b6c03748f035828b0a86ee9c588173e)