Question

Which set of polar coordinates describes the same location as the regular coordinates (-5,0)? A.(5,90) B. (5,0) C.(5,180) D. (-5,270)

Answer 1

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.