Question

Which polar coordinates represent the same point as (3, π/3)? (Select all that apply.)

Answer 1

(−3, −2π/3)
(−3, 4π/3)
(3, 5π/3)
(3, −π/3)
(−3, −7π/3)
(3, 7π/3)

Answer 2

I only selected the last one but there's more

Answer 3

have you tried drawing it out?

Answer 4

Would it be the last 3 only?

Answer 5

if you take the time to draw out each of the polar coordinates, then you should have your answer

Answer 6

But they're all right triangles...

Answer 7

Where on the polar coordinate graphs do those points lie? They're not right triangles at all, they are just points on a graph, single 0-dimensional points. Just like on a cartesian coordinates graph, there are points, so are points on a polar coordinates graph

Answer 8

keep in mind that \(\bf \cfrac{7\pi}{3}\implies \cfrac{6\pi}{3}+\cfrac{\pi}{3}\implies 2\pi+\cfrac{\pi}{3}\)

Answer 9

I don't know much about polar coordinates so...

Answer 10

\[(r, \theta \pm 2n \pi) \quad \text{and} \quad (-r, \theta \pm (2n+1) \pi)\] will all represent the same point: (r, theta) where n = 0, 1, 2, 3, .... (integer)

Answer 11

@jdoe0001 so the last one should work, right?

Answer 12

Cartesian Coordinates (X-axis point, Y-axis point)
Polar Coordinates (Radius from origin point, How many units traveled in Radians(Unit Circle) point)

Answer 13

But the second to last one shouldn't work...?

Answer 14

The second one will work. Putting a negative in front of r and adding pi to the angle will represent the same point.

Answer 15

So would the first one work?

Answer 16

The first will work too.

Answer 17

So when r is positive, add/subtract 2pi, when r is negative, add/subtract pi?

Answer 18

exactly.

Answer 19

multiples of 2pi and multiples of pi

Answer 20

So it's only the first two, the fourth, and the last one?

Answer 21

or you can simply draw each one out as suggested before.

Answer 22

pi/3 = 60 degrees
2pi/3 = 120 degrees, etc.

Answer 23

-r is same as +r in the opposite direction.

Answer 24

Sooo... those aren't the answers? I'm still confused cuz I thought those were the answers based on this but it's still not accepting and I have one try left. The remaining ones dont look like answers...