find-the-rectangular-coordinates-of-the-points-whose-cylindrical-coordinates-are-a-4-pi-32mathrmb5-p

Name: find the rectangular coordinates of the points whose cylindrical coordinates are a 4 pi 32mathrmb5 p
Uploaded: 2020-07-16
Duration: 5 min 13 s
Channel: Numerade
Description: Find the rectangular coordinates of the points whose cylindrical coordinates are (a) $(4, \pi / 3,2),(\mathrm{b})(5, \pi,-4)$

Question

Find the rectangular coordinates of the points whose cylindrical coordinates are (a) $(4, \pi / 3,2),(\mathrm{b})(5, \pi,-4)$

Paul Teng · Accepted Answer

Okay, so this farm wants you toe convert a couple of Solyndra coordinates into rectangular coordinates. So a solid record ascender. Thus, Linda cornice are in terms off our data and see where Arteta is. Ah, the polar coordinates of the projection of a point onto the X Y plane and Z is just ah directed distance from the X Y plane to the point so we can use these formulas here to convert the cylindrical coordinates into into rectangular coordinates. And you can notice these two for mills. These two foreigners him used convert polar coordinates which are in two dimensional into McCain record minutes. So we have here for pie thirds negative too. If we were to plot this, it would have in our value of four. So it would be a distance of four from the pole. So 1234 beard distance of four from the pole. The data is pie thers, which mean it rotates. The point is rotated pi thirds radiance from the polar axis, which is the positive X axis. It&#x27;s rotated counterclockwise. So if we were to rotate pi third, that would be somewhere around here somewhere around here and this would be Piper, is this. There&#x27;s some angle. And finally Z is negative two, which is the distance on the Z axis. So negative to would be two points downwards. So your point would be somewhere here in that quadrant. So if you were to convert this into you can either coordinates, we need to use the form owes. Let&#x27;s do that To calculate X, we have to use our coastline data where ours for and data is pi over three. In this Sequels to to cause co sign a pi over three is 1/2 before time. One has to exactly why I need our sign up that also ours for data is pi over three. Sign of pi over three is Sarath 3/2. So you would end up with a Y of tour at three. And finally disease Josie souls you would equal to negative two. So our answer in terms of X y Z would be to come a two round three comma negative too. This would be your final answer for part A. If you want to check on the plot that we moved a distance of two on to move this insult to on the X axis and we moved a distance to on the Y axis a distance of two. On the the negative tone of the access, you will find yourself in the same region of as we plotted. So that&#x27;s how you can check to make sure we did everything correctly. So this is part B. Part B is converting the courts under coordinates to negative, however, to one into retaining their coordinates. For his part, this first So our is ah, value of two. So I mean it is a distance to from the poll data is negative pi over tomb. That means we&#x27;re rotating it clockwise instead of counterclockwise pirate to radiance or 90 degrees so it would be rotating to so it would rotate to the negative y axis. So that would be an angle pi over two. And finally, it&#x27;s ah, the value of one has the value one. So that&#x27;s the value one. So your point would be somewhere here above battling. So now that we&#x27;ve gone in our point, let&#x27;s convert it in to retain their coordinates. So X equals to our coast. I take it off where our is to and co sign off. Beta. Martha is prior to goes on. A pirate too is zero. So we have an X value of zero. Why? Why is equal to To sign off data where there is negative O negative, Piper Till so sorry I messed up here. That should be a negative Colson. A coastline of negative high over to but thats zero so off sign of negative. However, to is negative once or two times a day. And one is negative. Two for your wife value. Finally, these just seem so Z equals to one. So your answer in terms of X Y Z is zero you too one. And if you look on the quiet, you can see if we it is indeed zero on the X axis. Make it two on the Y axis and then one on the easy access. So that&#x27;s how you can tell me Did that correctly

Wen Zheng · Answer

The problem is plus the point. Who&#x27;s cylindrical? Coordinates are Cuban. Then find it. If the rectangle coordinates off the point at a war pyre with three and nicked it too. The four part eh? We can a lot of the point as follows they dies, they go to pie or three silver. Half this is Pi over three and our is equal to four. This is called for Andi. See if he got connected to selective too. So it&#x27;s a point or hi. Over three and victim too, is rectangular. Coordinates are Max is the control or Tom&#x27;s Co sign high over three, which is not true. Why is he going to four time sign? Hi. Over three witches he go to two times Root of three. Andi thes e called Connected to that too. To tam through two three on detective two is a rectangular coordinates of the point how to be two next to a pie or two and one so they can plan to the point as follows. That is the go to next. You pi work too. So here on DH eyes, there were two, three, six one. This&#x27;s a point to neck to pie over two and one. It&#x27;s rectangle. Coordinates are X is equal to two times co sign negative high over to which is equal to zero. Why&#x27;s he called true times? Sign next to your pie over to which is connected to on see if they got one zero negative two and one is a rectangle coordinates off the point.

Chris Trentman · Answer

So we are given the spherical coordinates of a point and rest to plot this point. Then we&#x27;re asked to find the rectangular coordinates of the point. Spiritual coordinates of the first point are too sure. Hi over to so pi over two years now to graph this. Yeah. No we&#x27;re gonna draw our X, Y and Z axes. Alright kid. Right be sending now because data and fire are both between zero and pi. Well sorry fi is pi over two. So we&#x27;re in the xy plane. In Theta is pie or two. So we&#x27;re in the first quadrant of the xy plane. Yes. Yeah alcohol sweet. It&#x27;s a bit like oh B C. Well that&#x27;s you know that&#x27;s Evan. What? Right. A lot of fun. Well James was the since data equals pi over two and five equals pi over two were on the positive Y axis. So the point is located about here. That is the. Now find the rectangular coordinates because they do this graphically. Or we could use the formula for spherical coordinates. So we know that X equals road times the sine of phi times the co sign of data boxing. It&#x27;s a sex. This is two times the sine of pi over two times the co sign of pi over two, which is zero. Why is equal to rho times the sine of phi times the sine of data, which is two times the sine of pi over two Times The sine of pi over two, Which is equal to two and Z is equal to rho times the coast Sine of phi, which is two times the coast. Sine of pi over two which is zero. Therefore in rectangular coordinates the point X. Y. Z. Is 0- zero. Mhm. Then in part B. Were given The point in spherical coordinates for negative pi over four. Hi over three. Never fucked kids. It&#x27;s just getting one asked with the this island in the caribbean right? Like. So we have that row is for data is negative pi over four and five is pi over three. Since five pi over three where above the Xy plane. Since data is negative pi before this means we&#x27;re above the Xy plane and in particular were above the fourth quadrant. The words that that Since Roe is four, we&#x27;re at a distance for from the origin. They were like Olivia guns. Old boyfriend faked his own death. Mexico, yep. Yeah. Come on Bruce. Yeah. Mhm. Well, nick you hear about this? I&#x27;m doing research. Read jesus christ. Great. We&#x27;ve been taught our engineer. Yeah. I don&#x27;t know what faked his own That he drowned like 10 years next year. Just the Yeah, avoid like child support. She was. Yeah. Louise. Yes. Finally yes to say yes. So first of all, rotate hi over three on the positive Z axis, negative pira for princes here, however, three of them we go up to about ah to hear maybe and then we&#x27;re going to be a distance of four from the origin. What? Maybe about here? Like first of all, what I love too is so in green. This is the position of our point. Yeah. His point is cadence. You&#x27;re got it. Now. To find the rectangular coordinates. Will use this spherical coordinate equations. We have X equals row times The sign of five times the co sign of data. This is four times the sine of pi over three times the co sign of Negative Pi over four. This is four times no Route 3/2 times Route 2/2. This is Route six. Why is equal to rho times the sine of phi times the sign of theater, which is four times the sine of pi over three times the sine of Negative Pi over four. This is four times right Route 3/2 times Negative route to over two, which is negative Route six. Finally, Z is equal to rho times the co sign of fi, which is four times the co sign of pi over three, just four times one half, which is to therefore in rectangular coordinates. The point is that X. Y. Z equals Route six, Negative Route six two small, and those are no the most.

Chris Trentman · Answer

we are given the spirit of coordinates of a point interesting plot this point and then find the rectangular coordinates of this point spherical coordinates. Rove data. Bye. Our six pi over three however six to help us grab. I actually use rectangular coordinates. So if I&#x27;m rectangular coordinates, I use a spherical coordinates equations. We have X equals road times. That&#x27;s true Simon. If I time is the co sign of data, just six times Sine of pi over six And is the co sign of prior to three. Six times one a half times one half which is three hats. Why is equal to rho times the sine of five times the sine of data. Just six times the sine of pi over six times the sine of pi over three. just six times one half times. Route 3/2 which is and the I think three, route 3/2 can&#x27;t and Z is equal to Rho Times the closed sign of five. Just six times the co sign of Pi over six. Just six times and like shit. Yeah. Route 3/2 which is 3 3. Their former tacular coordinates. The Point X. Y. Z. Is rehabs three. Route three over to and 33 Georgia is so to plot the point. You can use these coordinates or use the spiritual coordinates. Yes. Yes. Now because by is pie over six. We are going to be above the XY plane. His theater Is Pi over three. Yeah. Then we end up in the second quadrants or above the second quadrant which are groping them without like how kind of the defense. Yeah because it&#x27;s Yeah we&#x27;re the hornets. Yeah. Your entire identity is based. You&#x27;re inherently a sec. Yeah. So you rotate hi over three work. You know what? We&#x27;re only rotating pi over three sore in the first or above the first quadrant. Actually I I thought you were like years of. Is that this thing Part of human behavior? Yes, somehow. Yes. Having Now we&#x27;re a distance of six from the origin. Fine. I Great. Great. This is I mean this. Yes. Right. Right. Sure. Right. Every every All right. Breaking news. Someone just, you know, I mean it&#x27;s. So what do you think the smallest thing I like to click me? They did. So is that the point about here?

Wen Zheng · Answer

The problem is plots a point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point at a square root of 23 Power four and two so we can plot the point as follows. Fed eyes. We go to three pi over four. Wow, yeah and R is equal to squad relative to 30 to 2. So that&#x27;s the point. It&#x27;s rectangular. Coordinates are X is equal to the square root of two times co sign three pi over four, which is equal to negative one. Why is legal to squads of two times sine three pi over four, which is equal to y and the C is equal to true. So the point next to 112 is rectangular coordinates of the point. Hard to be 0.111 The first we can plot the point as follows Here, data is equal to one. Get fitter is equal to one and our is also equal to one. These also equal one some of the points here This point the rectangular coordinates are X is equal to one times co sign one which is equal to cosine war. Why is equal to one times. Sine one, which is equal to sign one C is equal to one. So so point sign one sign one and one is rectangular coordinates of the point.

Problem

Perform the indicated operations involving cylind…

Problem 32 Easy Difficulty

Find the rectangular coordinates of the points whose cylindrical coordinates are (a) $(4, \pi / 3,2),(\mathrm{b})(5, \pi,-4)$

Answer

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