For this problem of our goes one plus Jose data. We are first going to graph it. Let's grab it right over here and we know this is actually a polar graph. You know, it's polar. From the fact of in fact it's trick and from what they did in the problem. So I'm gonna call this my center. Yeah, if you graph it on any graphing device that you have, it's actually going to turn out to something like this. It has a little pinch right here. This is something that I call a cardioid. Um and a cardioid is one of the few polar types of graphs that are out there other than say circle. And we know a cardioid when we see it's almost a circle. But not because of this pinch, a cardioid, it's met when it's typically in the form of this type of equation given it has to be in the form of one plus or minus coat Cynthia to or one and plus or minus same data, it cannot be 10 because if we did tan then this would be spiraling all over the place. But And you see that A I put right here now the A. And this problem is just one. There's always going to be a one in front of a trick if nothing is there. But in case there is another number, there a has to be greater than zero to like I said in this problem a close one. So it's always important for these to meet the requirements of a cardioid. Now, in order to go on about so much uh putting it into its summer trees and putting it into its Cartesian form. What I'm gonna do is draw out another craft. This time it's actually going to be something that resembles a polar to a Cartesian. So right here, I'm gonna do is draw disappear here. So this right here is actually are this is X. And this is why, as we can imagine with every triangle, you have a data. So this right here is what I call Polar to Cartesian. So when you were doing Polar to Cartesian or even sometimes to a Cartesian to Polar. Typically not though it's we're always referencing to this graph. When we're doing a Polar to Cartesian, we want to make sure that we're doing it in the right fashion and sometimes they might need a visual representation to make sure we're doing it right, especially without these trig equations in front of us. So that's why I dropped this graph is because oh, it might be easier to reference, say a triangle instead of all these other equations in front of us. That can get us quite puzzled at times. So what I'm going to do next is actually rewrite our equation. But this time I'm going to right out some other key equations off to the side. So we have art squared, let's X squared plus y squared. I know that we also have tan data, bulls, Y over X. And then we know that X equals our coastline data. Why equals r signed data. We're working with points. It's always the co sign fine. So those are typically some equations or something. So you want to have an art toolkit, whether it be, like I said polar to Cartesian or Cartesian to polar. So one sweater going to transition this to Cartesian. One of the first equations. Well, what we want to do is take probably this one, this one and this one, it's important to distinguish which ones you want. And the reason why is because you don't want you just get yourself too much in a struggle. Because we know we're not working with the point, we're not working with tangent so why even look at them or whatever. I'm only going cross them out so you know they exist. But we want to make sure we distinguish which ones we have. So with this in mind I'm going to actually rewrite this equation right now because sometimes we don't actually use it in its exact form. What we do is we actually square rooted. And the reason why we do is actually to just get it to our okay, we don't want to have to deal with R squared if we're trying to find our and so what we're going to be doing first is with this equation. Our first step. It's too multiply both sides are I'm gonna be abbreviating the steps so we'll have R squared equals our times one plus co sign peter. If we so break this out then we'll have our plus our coastline. The art scored still stays the same. No we got a substitute. That's our next step two. And we want to get rid of these ours. Especially because whenever you see A. R. It's mainly in polar form. So what we'll be doing as far as they are squared, we know that. Okay we have the expert. That's why I squared the or in itself. That's why we have the square root form X. Squared plus Y. Squared plus our cosign theta. That's an X. And then that's actually our final problem. So it may seem so many excuses lives. It's like oh my gosh there's so many squares believe it or not. As long as it's an X. And Y. Form, that's our answer. So knowing of everything there, you could try to re put it back into Polar to verify your answer. And sometimes teachers do encourage that to double check to put it back into polar form. And then if you're starting a petition, Parton Polar put it back into Cartesian, that's up to you on your own time and everything like that. So I do want to encourage you to do that on your own time and that's actually how you solve a polar equation into Cartesian and graf eh polar equation as well.