00:01
So in this problem, what we're being asked to do is determine which of the following pairs of coordinates that are in polar form would not represent the same point in polar coordinates.
00:11
Okay.
00:12
So keep in mind how polar coordinates work.
00:15
So we have our system and we have our circles.
00:18
That is referring to our r values.
00:21
So let's look at our first one.
00:23
Let's say we have r and theta.
00:24
So let's just come up with an example.
00:27
Let's say we had two and then our angle.
00:29
Let's say that we'll say that we'll.
00:30
Was pi over four.
00:31
So how would we graph this? well, it would be on the second circle and pi over four that's at the angle in the first quadrant.
00:37
That would be about here.
00:38
So let's apply this to our second one.
00:40
Well, that would be negative two and pi over four plus two pi.
00:43
Well, adding two pie is just going to give us the same angle because remember, that would be a coterminal angle.
00:49
So we would start at negative or that same angle, which is pi over four.
00:54
But remember, because our radius is negative, would now be on the opposite side if we were to draw a line.
00:59
So notice it would not give us the same one.
01:01
So a is going to be one of our answers.
01:05
Let's take a look at b now.
01:06
So we have r and theta, and we're trying to compare this to negative r and theta plus pi.
01:14
Well, let's think if we use the same example as before.
01:16
So remember, two and pi over four is here.
01:19
So now we have negative two and pi over four plus pi...