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(q Given two polar curves 11+ 4cos 0 and 126 for 0 < 0 < 2t.Sketch the curve of r1 and 1z:2 marks)ii) Find the angle(s) of intersection between the two curves...

Question

(q Given two polar curves 11+ 4cos 0 and 126 for 0 < 0 < 2t.Sketch the curve of r1 and 1z:2 marks)ii) Find the angle(s) of intersection between the two curves.marks)

(q Given two polar curves 11 + 4cos 0 and 12 6 for 0 < 0 < 2t. Sketch the curve of r1 and 1z: 2 marks) ii) Find the angle(s) of intersection between the two curves. marks)



Answers

Find the polar coordinates of the points of intersection of the given curves for the specified interval of $\theta$. $$r=2+\sin \theta, r=2+\cos \theta ; 0 \leq \theta<2 \pi$$

The following problem. We're going to sketch the curves and find the point to which they intersect. And we want to express the answers in rectangular coordinates. So this is going to be are equal same data and then articles a negative coaching theater. We see that the intersection points are going to occur when signed data equals and negative coastline data. And we know that occurs a couple of different places. So we see that there is an intersection at 00. And then we also see that there is an air section Right here. So we know 00 makes sense because if the radius is zero then we'll see that to be the case. But here we also see the intersection when the angle is um when the angle is this pi over four to pi three pi before because then signed data equals negative co Cynthia to so that ends up giving us our final answer for that. And then we can also look at intersections between other curves such as our equals the square root have signed data and um 2- Sign Data. There are other options that we have um where this is also my sm plus so that would be the one intersection point here at 01. And then there's other options. But we want to make sure we express our answers in rectangular coordinates which shouldn't be difficult because when we graph these, we see that this will be in rectangular coordinates. I'm on a plane

Go Geo side. Your data are just with a few core Santa. Do you find that intersection region a Jew? Girls were set them ago. Therefore him decide your teeth. Are you go? Just credit to Kasai Tita. We know Low side Judita ago. Judah juice idea. Go cited that you could just get too excited. And now bringing new home Julie on this side front of the ghosts I tita outside and then we should get inside with two site data and then ah, minus created to do you could use a row isn't implies that go cited an echo Ju zero on the site teatime us Nico two squared up Jew on Jew and for the first gay in it to have a causative ako ju zero means that Thomas Skakel chip out of you and the three Bryant Jew. But because Sandra detained between the Georgia Pie only that's we mean a solution for the first case For the second case in it you have site ego juice with your to think Thomas Incontro pie out of far. And from here we can find a problem intersections. It will send the band of doing do the 1st 1 here. Then we get some plank, which is there also will be is up to now. It was sent to the 1st 1 we set. We have the sound a pint of to and then it goes to one and the price fall.

The following problem. We're going to sketch the curves and find the point to which they intersect. And we want to express the answers in rectangular coordinates. So this is going to be are equal same data and then articles a negative coaching theater. We see that the intersection points are going to occur when signed data equals and negative coastline data. And we know that occurs a couple of different places. So we see that there is an intersection at 00. And then we also see that there is an air section Right here. So we know 00 makes sense because if the radius is zero then we'll see that to be the case. But here we also see the intersection when the angle is um when the angle is this pi over four to pi three pi before because then signed data equals negative co Cynthia to so that ends up giving us our final answer for that. And then we can also look at intersections between other curves such as our equals the square root have signed data and um 2- Sign Data. There are other options that we have um where this is also my sm plus so that would be the one intersection point here at 01. And then there's other options. But we want to make sure we express our answers in rectangular coordinates which shouldn't be difficult because when we graph these, we see that this will be in rectangular coordinates. I'm on a plane

You got three. The other one are included at your plus juco Santita that you find the intersection Agility person would amico for three. A coaching job. Plus, Joko Santita means that Cassetti time we ego do the one other Jew and it means that jugend acoustic today. Could you have You must be called you. And, uh, this one will be 60 degree Tita and we're ICO Jude. Uh, 300 degree. And then from here we can find it. Two intersections. The 1st 1 will be a 3 60 degree. No known one will be three and 300 decree.


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