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%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001307Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=e5c98f34bf7d0fde33c11672c1cbf87f0a703e4e502399df46e98b8e65642187)
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%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001307Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=f30203dbb84c0145c1733834d826ef76f46db3956ff72b61ec13ba79f65c4ab5)