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The polar form of the circle with radius 2 and center (0,2) isa)r =2 sin 0 +2cos 6b) r = 4cos0c)r = 4sin 0d)rsin8 = 2...

Question

The polar form of the circle with radius 2 and center (0,2) isa)r =2 sin 0 +2cos 6b) r = 4cos0c)r = 4sin 0d)rsin8 = 2

The polar form of the circle with radius 2 and center (0,2) is a)r =2 sin 0 +2cos 6 b) r = 4cos0 c)r = 4sin 0 d)rsin8 = 2



Answers

Sketch the graph of the polar equation. $$r=6 \sin ^{2}(\theta / 2)$$

Yeah. First we can rewrite this equation in this expression so how we cure this expression first because that course and said I. E. Calls Coulson square the half of this young girl miners sine squared the half of this uncle. Everybody knows that. Co sign square data. Sine squared equals one and hence this part he calls this part. And now we can come by the seminar terms and we solve for this term. Not that The sine squared set our two is similar and we just to substitute district you know then we get this result and now I draw a table which contains the ST interval and the corresponding value of office for the first interval with data is from Their road to pi over two Power is from 0 to spring and in the graph it's a sprint and for the second in girl it says Perp's And then the 3rd Angel. And mm most dangerous.

Mhm. First we multiply both sides of this equation by our that is our square rico. Six times are co signed Ceta miners. Two times are assigned seating according to the relationship between polar coordinate rectangular coordinates. Our square equals X squared plus y squared. Our call sign ST Michael's ex in our science at Pecos, Y. Now they can subtract the right hand side from both sides and this becomes X squared. My nurse six x plus Y squared plus two. Y. You go there and now we can't add nine And then out of one to the left hand side And make sure 10 to our right hand side as well. and now there are two perfect square in the left hand side, waitress, X -3 Squared class. Why? Plus once we're close to this is the creation of the circle and the center of this circle is at great minus one. And the radius of the circle is the square root out.

Here. We're looking at this graph. We see that this is a rose girl with three particles. So the standard equation off Rose girl off. This type is r equals be signed and Tita therefore firstly, since they know that there are three patterns off this rules so we can say that three back those oh rules girl, since three easa or number therefore the value off and is three now we can see bed. Ah, the length off a rose petal is to therefore b will be to now putting both these values in our given standard equation, we get our equals to sign three Tita Therefore, option D, which is r equals two signed three Tita is correct.

So remember we said that we can find this angle beta by saying by finding tension of two veda. So we confined. Beta is equal to question mark by saying Tangent of two beta is equal to be over a minus seat. So he said, Be in this in this The scenario is your also B is equal to zero since we don't have an X and Y term and we said a is equal to is equal to one and C is equal to one. So we have 0/0, which is undefined. And so now we wanted we want we know that two beta tangent of two betas equal to 90. Well, Tangent of 90 gives us an undefined and so to bed is equal to 90. Whoa! Beta is equal to 45 degrees. Or or let's say pi over four. Right? And so this is our angle, Beta. This is our angle, Bater. Well, then we have now we have weaken complete the square to make this look more of like a a circular problem. And we can verify that this circle goes through the origin by plugging and zero, so we would have zero plus zero minus zero minus zero. This is, in fact, equal to zero. So we've checked that the circle circle goes through origin and if we complete the square here we have we get X squared minus six, route to x and then we have be over two square. So we have three three Route two squared. So this gives us plus and three route to square gives us nine times to, which is 18. And so now we want to find two numbers that that multiplied to 18 which is which is three were too. And add up to negative six through two. So this gives us X minus three, Route two squared plus. And then we have the same thing for why we have y minus three route to squared. So this gives us this gives us this is equal to and since we remember, since we added 18 to both sides, we have to add 18 to both sides here. So we have 36. So we know that our radius now radius is equal to to six. So now we can put this in in polar form, so we know our should be equal to two times, the radius with just 12 times co sign of data, coastline of data. And then we're gonna keep this in radiant. So we say data minus hi over four. And so this here is our solution.


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