 In this video, we provide the solution to question number one for practice exam number four for math 1220. In which case we can find the polar equation to match the provided graph here. And this is in fact a polar graph. It's some type of limouson. There is an inner loop here. You could try to use some formulas that we've seen to try to grab this thing. But honestly, the best bet here is just process of elimination. So four points will be interest to us will be the four quadrantial angles here. If you have a zero angle, notice this gives you the point where your radius is equal to two. When you have pi halves, like so, this would give us a one, two, three, four, five radius. On the left hand side, you also get a radius of two when the angle is pi. And then here, because of the inner loop, you actually get this negative radius of one when the angle is three pi halves. So when you're at zero, you get two. When you're at pi halves, you get five. When you're at pi, you get two. And when you're at three pi halves, you're going to get negative one. So that itself can actually help you with these things because at the very least you can plug those things in here. So like when if you just take, for example, when the angle is zero, that eliminates a lot of these. When the angle is zero, cosine of zero is equal to one. Sine of zero is equal to zero here. So notice that if you plug in zero, it's basically like cosine disappears, you get two plus three, which is five. That's not two. So it's not that. When you look here, if you plug in zero into sine, you get zero. So this term is vanishes, you get a two. So B is a possibility here. Here you're going to get five again. So that's a no. Here you're going to get six. That's a no. Here you're going to get three. That's a no. And then lastly, you're going to get three again, which is a no. So honestly, just by using this one observation, when the angle is zero, the radius is two, this actually leads to the correct observation. Now if that didn't rule out all of them, using the other three points will eventually rule it out. If you just look at the quadrantial angles by process of elimination, you'll find the correct function. But heck, we did it with just the first one.