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Use polar coordinate system to plot the point with the given polar coordinates: Then find another representation (r,0) of this point in which: r> 0, 21 <0 = r...

Question

Use polar coordinate system to plot the point with the given polar coordinates: Then find another representation (r,0) of this point in which: r> 0, 21 <0 = r<0,0<0<21. r> 0, 21 < 0 < 0.(1o5) Choose the correct graph below:Click to select your answer and then click Check Answer:3 parts remainingClear AllCheck Answer

Use polar coordinate system to plot the point with the given polar coordinates: Then find another representation (r,0) of this point in which: r> 0, 21 <0 = r<0,0<0<21. r> 0, 21 < 0 < 0. (1o5) Choose the correct graph below: Click to select your answer and then click Check Answer: 3 parts remaining Clear All Check Answer



Answers

Plot the point that has the given polar coordinates. Then give two other polar coordinate representations of the point, one with $r<0$ and the other with $r>0$ .
$$
(-1,7 \pi / 6)
$$

In this problem, You're given the 0.31 Now, this is not written in terms of pie, so we're gonna have to do some approximations here. Here's my polar graph here. Zero. Normally, this is pi over two, which is approximately 1.5 seven. This is pi, which is approximately 3.14 So if I rotate one unit gonna put me about here if I march out the replaces. This is the original location of the point. Since this is the original location of the point of 31 I can get to the same location by rotating an extra half a circle. So I would do negative three. Because I have to walk backwards three units, but more. To get that rotation, I would have to rotate half of a circle, which is pie radiance. What I mean by that is the distance from this grade two. This ray is pie units, so one plus pi would get us in that location. Now, I could also go in the other direction as well. Okay. One of the things that I would have to do is I would have to go backwards a full rotation or to have a positive our value. So in this particular case, I would have to do, um, two pi. So if I start here and I rotate backwards a full direction, I'm going to have one minus two pi. That would mean I would start at this green line and I go backwards. One full rotation, and that would get me back to the spot. And this would be another rotation. So your two possible solutions there are more, but these air

Okay. First we want to plot this 0.3 pi over two and then find two other names for one with the positive are and one with the negative are. So first I'm gonna find pi over to which, you know is 90 degrees. So here here's the pi over to line and then from the center, go out three circles. 123 And then there's my point right there. Three, however, to Okay, so now let's find another name for it. If our is gonna be positive, it has to be three. Okay, so three. Okay, we could start here and go all the way around once. That's two pi plus pi over two again. So two pi plus pi over two. Get a common denominator. Add those together three and five pi over two. Okay, Now let's give it another name on Lee. Let's give it a negative. Are so for a negative, art will have to be negative. Three. Okay, so then you have to go across Thio. Get that mess over there. Host, Fight over to that one. Okay, so for it to be a negative radius, then we have to be coming from this angle. So we go all the way here to three pi over two. And then instead of going out three this way, we're going to go through this way to three. Okay, so it's other name is negative. Three. Three pi over two. Okay, There's lots of other names we could call it. Negative. Three. Negative pi over two. We could call it positive. Three. Go around again. Nine pi over two. There's all kinds of names that are correct for this.

So in this problem were given the point three com a pi over two. So let's plot that first before identifying some other points. So pipes, we have zero. We have pi over two, and we have a roti a US 123 units out. So here's my original location now, and I can get there many, many ways one way, which will have an R value that's positive. Instead of rotating in a positive direction, I can rotate in the negative direction, the rotating negative direction. That's negative. Pi over two negative pie negative three pi over two. So I could have another point that would be three and negative three pi over two. This as a positive, our value. Now, I could also rotate negative pi over two, but then march backwards, having a negative our value. So another possible solution would be negative pi over two, which would be a 90 degree rotation down here and then back up three units here. Two other possible, uh

In this problem. I'm given negative chew and negative pi over three working on my polar grade. I'm gonna rotate into thirds here. I'm gonna rotate negative pi over three and I'm gonna march back to units. So in order to get to the same location, I can get there with a positive our value of two. If I rotate in a positive rotation pi over three two pi over three. I can also get there by rotating in a positive direction all the way over here by thirds. We've got pi over 32 pi over 33 pi over 34 pi over 35 pi over three. So I could also rotate five pi over three and back up two spots. This has a positive our value in a negative. Our value with possible rotations. There are an infinite number of solutions, but here, just two of them


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