The correct answer is:
(5, 180°).
Explanation:
To convert polar coordinates in the form (r, θ) to rectangular coordinates in the form (x, y):
x = r cos θ
y = r sin θ
For the first choice, (5, 90°):
x = 5 cos 90 = 5(0) = 0
This is not the correct x-coordinate, so this does not work.
For the second choice, (5, 0°):
x = 5 cos 0 = 5(1) = 5
This is not correct; we want x = -5.
For the third choice, (5, 180°):
x = 5 cos 180 = 5(-1) = -5
This is correct. Now to check the y=coordinate:
y = 5 sin 180 = 5(0) = 0
This gives us the correct coordinates.
