Which of the following gives all possible coordinates of...

Which of the following gives all possible coordinates of polar coordinates \((-5, -\frac{1}{3}\pi)\)? ? \((5, -\frac{1}{3}\pi + 2k\pi)\) and \((5, \frac{2}{3}\pi + 2k\pi)\) ? \((-5, \frac{2}{3}\pi + 2k\pi)\) and \((5, -\frac{1}{3}\pi + 2k\pi)\) ? \((-5, -\frac{1}{3}\pi + 2k\pi)\) and \((-5, \frac{2}{3}\pi + 2k\pi)\) ? \((-5, -\frac{1}{3}\pi + 2k\pi)\) and \((5, \frac{2}{3}\pi + 2k\pi)\)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 If r does not equal to zero, which of the following polar coordinate pairs represents the same point as the polar coordinate r theta? so let's think about this for a minute.

00:11 If we have the same r, then we can have any theta that is coterminal to that particular theta.

00:20 So that means if we're dealing with radians here, to be on the coterminal here, i would take theta plus some multiple of 2 pi.

00:31 And i would multiply that by one or any integer, and it would be coterminal.

00:37 So that means we could have 0 plus 2 pi or mean theta plus 2 pi, theta plus 4 pi, theta plus 6 pi.

00:46 If we're in the negative, we could have theta minus 2 pi, theta minus 4 pi, etc.

00:53 So the first thing i'm going to do is look at my angles and see which is the same as our theta.

00:58 So we have theta here, theta, that's going to be the coterminal.

01:03 That's an odd, so that's not going to be coterminal.

01:06 And then i look at this one as an odd.

01:08 It won't be coterminal.

01:09 This won't be coterminal.

01:11 So if they're coterminal, then we have to have the same r.

01:16 So we could do r and then theta plus some multiple of 2k of 2 pi.

01:26 So when i look at that, i say, well, neither one of these have the same...

Question

Please give Ace some feedback