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

Solution:

We have to find the set of polar coordinates that describes the same location as the regular coordinates (-5, 0).

We know, the polar coordinate is (r, θ)

To convert polar coordinates to rectangular coordinates in the form (x, y)

x = r cos θ

y = r sin θ

From the options,

A(5, 90°)

r = 5, θ = 90°

x = 5 cos 90° = 5(0) = 0

y = 5 sin 90° = 5(1) = 5

Therefore, option A is false.

B(5, 0°)

r = 5, θ = 0°

x = 5 cos 0° = 5(1) = 5

y = 5 sin 0° = 5(0) = 0

Therefore, option B is false.

C(5, 180°)

r = 5, θ = 180°

x = 5 cos 180° = 5(-1) = -5

y = 5 sin 180° = 5(0) = 0

The polar coordinate

Therefore, option C is true.

D(-5, 270°)

r = -5, θ = 270°

x = -5 cos 270° = 5(0) = 0

y = -5 sin 270° = -5(-1) = 5

Therefore, option D is false.

Therefore, (5, 180°) describes the same location as the regular coordinates (-5, 0).

---

Which set of polar coordinates describes the same location as the regular coordinates (-5, 0)?

Summary:

The set of polar coordinates that describes the same location as the regular coordinates (-5, 0) is (5, 180°).