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Convert the given polar coordinates to Cartesian coordinates: (-9, 559v3 29 2(x,Y) =...

Question

Convert the given polar coordinates to Cartesian coordinates: (-9, 559v3 29 2(x,Y) =

Convert the given polar coordinates to Cartesian coordinates: (-9, 55 9v3 2 9 2 (x,Y) =



Answers

Convert the given Cartesian equation to a polar equation
$x^{2}=9 y$

Okay, so this we want to turn y squared equals nine x into a polar equation. Right? And polar equations have are So we're gonna substitute these equations that X equals our coastline. Data on my ankles are signed data in for their respective variables, and then sulphur are, and that should give you a polar equation. So first things first. When I plug this in, I say, OK, why is really our sign of data and that squared equals nine times our coast? I am data, okay? And so now I'm just gonna kind of write out what it means. That's r squared. Sine squared of theta is nine. Our coastline data like. So now when you've got ours on both sides, you wanna put him on the same side. So I'm going to subtract this nine are co sign data from both sides and I and our coastline data. Okay, so now over there, it's gone. Which leaves us with a zero when we get our squared sine squared. Data minus nine. Our coastline data, It's a little squishy. Well, hurry and fix that equals zero. Good. Okay, so now what we're gonna do is we're gonna factor out in our since they both have one that gives me are signs squared minus nine. Co sign Vita equals zero. Okay. And when I've got two things that are being multiplied to be zero right, one of them or both have to be zero. So that means this part is our equal zero. But that doesn't really help me, So I'm gonna set this side equal to zero as well. So r sine squared data minus nine co sign data. So, like that equals zero. And I'm gonna move everything toe one side except for my art. So I'm gonna add this nine coastline data back to the other side nine coastline data. I get our moves, not r squared r sine squared is equal to nine. Co sign data. Okay, Now I'm gonna divide by the sine squared, which gives me a one divide by signs squared, which on that side shows up and I get our equals. Nine coastline data signed Squared data. Now, since ours by itself. You can use that as an answer. We don't typically like to leave, um, signs and close lines infractions because they could be simplified, so I'm actually gonna come over here and say That's the same as nine. Co sign theta over. Signed data time. Signed data now co sign over Sign. That's the same is co tangent. So this turns into nine co tangent data over sign of data. Or I'm actually going to rewrite that as times one over sign of data because one over sign theater right there is really the c camp or Cosi cap Do that, right? Yeah. CO C camp when over sign Should be Cosi caf data. And so that didn't turn. Leaves me with nine co tangent. Seita. Sorry, I'm having a hard time right in Cosi can't data right? One over sign is the CO C camp. And that's how a lot of teachers like their answers because that's more simplified. You don't have your fractions. So from start to finish, that's how you do it.

We have all the number four and this we need to find the convert the police coordinate through Cartesian coordinates. Color coordinated nine comma 453 So this is our and this is peter. So Cartesian coordinate acts will be equal to are considered to nine cars for by battery and cause people's private tree. This will be in third quarter, so minus caused by victory is won by do well. This is -9 x two. Similarly, why will be equal to are saying peter so nine saying 45 x three. It will also be in 3rd Quarante, so This will be nine in to Rule three x 2. So X comma Y. In Cartesian coordinates Will be -9x2, comma 9, 2, 3 x two. Thank you so much. We should be dancer.

So the first thing we're gonna do is replace replace X with are coast I'm data. And why would our signed data then? We're going to group. Are are so have nine r squared times. Time sign data equals one. Then we're going to divide by nine Coastline data science they don't Both sides will have r squared equals one over nine co signed Data times Sign favor. And then one of our co sign is seeking one of our sign is co seeking so well, right. This as second data cozy container overnight. And then we'll just take the square roots of our equals square seeking. They had a coast Deacon Mehta over nine, which is the square root of second Data times because he can data over three.

Okay, Question 1 79 is us used to change the equation X squared plus y squared equals and nine into a polar equation. And this one is actually, um, pretty easy because polar equations air X squared plus y squared equals r squared or useful for our and take the square root of everything. So it be X squared plus y squared equals like so right. And so to do this, it's already in that form. Do you guys see how it kind of already matches up? So, like, here, you already have exports plus y squared. So that means nine is equal to r squared. So you can actually, like, stop your equation right there or you can take it one step further and say our equals three and you get that by taking the actual square root right? And so that's pretty much that you can leave as either one. They should both be acceptable. And this problem is pretty straightforward.


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