Hey, everyone. We know that the general shape of the graph of a rose has these sort of petals. So it makes sense that in order to actually graph a rose, we need to be able to figure out how many petals our rose has and where exactly those petals are located. Now we can do this easily by just finding one single petal and then determining the spacing of our other petals, which we can do based on the equation that we're given. Now this is exactly what we're going to do here. So let's go ahead and jump right in. Now remember that the equation of a rose will always be of the form r=a⋅cos⁡(nθ) or a⋅sin⁡(nθ), where a≠0 and nis an integer greater than or equal to2. Now the specific equation that we're tasked with graphing here is r=4⋅cos⁡(2θ), which I know is the graph of a rose because it's of this form, r=a⋅cos⁡(nθ). Now let's go ahead and get started with our very first step where we're going to look at our value of n. Here n=2 and 2 is an even number. Now whenever n is even, that tells us that we're going to have 2n petals. So if I take 2 here and multiply it by my value of n, which is also 2, that tells me that this rose is going to have 4 petals. Now with this in mind, let's move on to step 2 and figure out where that first petal is. Now, in order to figure out where our first petal is, we need to look at our value of a. In my equation here, I see that a=4, so that tells me that my r value for my petal is going to be 4 and all of my petals will be at the same length. So this will actually be the r value for every petal. Now we need to figure out what θ is for this first petal, which is determined based on whether our equation contains cosine or sine. Here our equation contains a cosine, so that tells us that θ here is going to be equal to 0. So I can go ahead and plot that very first petal at 4, 0, which will end up being right here. Now we can move on to step number 3, because now that we have our 1st petal, we can determine where our other 3 petals are. Now, that very first petal we know is located at 4,0. And we also know that all of those petals will be the exact same length. So I can go ahead and fill in 4 for all of those r values. Now I just need to figure out how these petals are spaced, which I can do based on the number of petals that we found in step 1. Now we found that our rose will have 4 petals. So here, if I take 2π and divide it by 4, that's how my petals will be spaced. This can simplify down to π/2. So here, if I take this 0 of my first petal and add π/2, that tells me that my second petal I can go ahead and plot at 4π/2, which is going to be right here. Then for my next petal, I'm going to add another π/2 to get me at π. So I can plot my 3rd petal here at 4π, which will end up being right out here. Then for my final petal here, adding another π/2 for that spacing, I end up at 3π/2. And I can plot that very last petal at 4, 3π/2. Now I have the positioning of all 4 of my petals. So all that's left to do is connect them with a smooth and continuous curve. Now I know that all of these petals will stem out from that pole because they're all coming kind of out of there to look like a flower. So my graph is going to end up looking something like this. Now again, remember, with all of these graphs, if you are asked to get more precise or if you want to get more precise, you can always calculate some more points, and that's totally fine. But now that we have fully graphed this rose, let's continue practicing graphing roses together. Thanks for watching, and I'll see you in the next one.