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(1 points) Giwen the points betvern and Q(Vz,m/4)(4,7/2) in polar coordinate, find tbe ditanae(15 points) Is the nrtorlite ucutulvinatio ofthe vrxtornfIc[[4(6) (20 ...

Question

(1 points) Giwen the points betvern and Q(Vz,m/4)(4,7/2) in polar coordinate, find tbe ditanae(15 points) Is the nrtorlite ucutulvinatio ofthe vrxtornfIc[[4(6) (20 points) Can nny vrtor [4€ R2 bve written nS n linenr combinat ion of the voctomuul

(1 points) Giwen the points betvern and Q (Vz,m/4) (4,7/2) in polar coordinate, find tbe ditanae (15 points) Is the nrtor lite ucutulvinatio ofthe vrxtor nfIc[ [4 (6) (20 points) Can nny vrtor [4 € R2 bve written nS n linenr combinat ion of the voctom uul



Answers

1-2 Plot the point whose polar coordinates are given. Then find
two other pairs of polar coordinates of this point, one with $r>0$
and one with $r<0 .$
$$\begin{array}{lll}{\text { (a) }(1,7 \pi / 4)} & {\text { (b) }(-3, \pi / 6)} & {\text { (c) }(1,-1)}\end{array}$$

We have given here the point that is minus 16 and fight by divided with food so we can find the really off guaranteed Also articles Tu minus 16 and take was toe five by divide with food. So X equals two article future. And why equals toe our scientist? So listen with, uh, minus 60 and course fight by divided with food and sign will be minus 60 inside five by divide with full. So now fired the value. So these are the coordinates 11.313 and minus here. So x way the corner car accepted 11.313 And why? That is minus eight. And now we can trace this point here. So he added, God, next system I can write it is here, and this point represented the 11 1313 And here this is the then 20. So this is 10. 20 also minus 10 minus 20. So see the point They did minus eight and 11 point today. So this would we? I guarantee it that it's 11.313 and minus it the point PD present 11 1312

Okay. So first let's plot a get you by over three pi over three is 60 degree. Okay, so let's proud this. So one two. Okay, so this is a point two pi over three. Okay and another two point is another two polar coordinates of this point is So first let's add two Pi to pi over straight. Okay. So I can't two and 75 of large three. Okay. And we can also. Okay so this is our is greater than zero. So let's make our change the sign off. The first couple that are okay. That is to and we add pie To power streets. I have -2 four pi over three. Okay, two for b. I have What? Pi over four. So this is what by this? Okay. 125 degree. OK So it is here right 225. So let's find one. So here is one. So this is the point we want. Okay 1 -3 Pi over four. So another two uh coordinator at this point is okay we add two pi two minus three pi over four. So I have one minus Phi pi uh one five pi over four. Okay and the other one is okay, so this is our greater than zero. So now let's change the side of our and at the same time we add pie to data. So uh this will keep the the coordinated the same as that's this. Okay, so we have this one Pi over four. Okay now we have a final one. For see we have minus one pi over two. So this is pi over two and we have minus one minus one is here. Okay so this is already are is less than zero. So now uh let's add two pi to pi over two. Okay so this is the same as this. I have -1 five pi over two. Okay. No let's uh this is for rs uh for our is less than zero, so now let's turn the sign of our to become positive. Okay so I have one and the let's head pi to pi over two. Okay so I have more one, three pi over two. Okay So this is the same as -1 power to.

We have given here. The point, minus four and five point of evidence is this is a polar coordinates. And now we have to press this polar coordinates and find other three points, so other three points will be so first, I'm tracing minus four and four, and this is fight by divide with food. So this is the surgical off r equals to four. So they hear the circle r equals to four things. And no, this would be the point. I can say minus r. And this is a traitor. Blessing minus And by and also, uh, and this is a recovering toe, Tita. Plus and minus two and fight. So now, minus are that it will you for and Kita I can hear, sir. Prick. Fight. So this will be the take down minus by. So treat other decide by do every six minus by will give minus by by 6.6. So one point will be here. We're four and minus by developing six. And also I can add also by. So this will fight by dividing six plus by So this will be the 11. So this is 11 by divide with six. So This will be four and 11 by divide with six. And also doing this with minus food. This can be done. I minus food and minus seven by They were Italy. And I put any of these three points. So this is a four and then minus by divided six. So this is a minus bi divide with six. So this is the point here four and minus by doing with all these three points represent the same here.

Okay. So that's part of the .5 times square to -11.5. Okay. So radius R. Is around seven. Okay. Yeah at the center is around one is 330°. Okay so I have the point which is so this is a point five times to go to the to -11 pi over six. Okay, that's right. Three other additional representation. The first one we add two pi to see to. So I have five times scored of two pi over six. The second one we achieved our two minus R. And we couldn't stay to to set a plus pi. So this is what we can't. Okay. And the 3rd 1 we have R. IC divide its two pi. They have five times square to to By just 11 pi over six. Okay. Yeah.


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