Hey, everyone. We're now familiar with the commonly occurring shapes that we'll encounter when graphing different polar equations, and now it's time to actually graph those shapes starting here with the cardioid. The general shape of the graph of our cardioid will remain the same with the orientation and positioning of it just changing based on the equation that we're actually graphing. Now remember that the equation of a cardioid will always be of the form r=a±bcos⁡θ or r=a±bsin⁡θ, where a=b. Now in order to actually graph a cardioid, we have only two things to determine. First, we want to determine the symmetry and then we simply want to plot points at our quadrantal angles. That's all. So let's go ahead and not waste any time here and just jump right into graphing this cardioid. We're tasked with graphing the equation, r=1+cos⁡β. I can tell that this is the graph of a cardioid because I have addition in this equation and this a value of 1 is equal to my b value of 1 because I have this sort of invisible one multiplying cos⁡θ. Jumping into our first step here in graphing this cardioid is to determine the symmetry. In order to determine the symmetry of a cardioid all we need to do is check whether our equation contains cosine or sine. Since our equation here is 1+cos⁡θ, that tells me that my graph will be symmetric about the polar axis, which is something that I should keep in mind as I continue into step 2 where we actually want to find and plot points at our quadrantal angles specifically. Remember that our quadrantal angles are 0, π/2, π, and 3π/2. Let's start here by plugging in θ=0 in order to find our r-value for this angle. Doing this, I get 1+cos⁡0, and the cosine of 0 is 1, so this ends up being 2. I can plot my first point at 2, 0, which will end up being right here on my graph. Now for my second quadrantal angle, π/2, plugging that into my equation, 1+cos⁡π/2, the cosine of π/2 is 0, so this r value is 1. I can plot my second point at 1, π/2, which will end up being right here. Then for my third quadrantal angle π, plugging in π to my equation 1+cos⁡π, the cosine of π is negative 1. So this ends up being 0. I can plot this point at 0, π, which will just end up being right at that pole because my r value is 0. Then for my final quadrantal angle 3π/2, I want to think back to my symmetry here. Because I know that my graph is symmetric about this polar axis, I can just take this point and reflect it right over that polar axis without having to calculate that value. So, that final point is going to be located at 1, 3π/2. Now we have all of these points and we can move on to our final step here which is going to be to connect everything with a smooth and continuous curve. We already know what the shape of our graph is. We know the general shape of a cardioid. And here we just want to apply that shape and connect all of these points here. Remember that a cardioid has sort of a bump at the top and then extends out. Our graph is going to end up looking like this. Remember that you can always calculate some more points if you want to get a bit more precise, but here we have fully graphed this cardioid. Now that we know how to graph cardioids, let's continue getting practice with this. Thanks for watching, and I'll see you in the next one.