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Identify the symmetries of the curves in Exercises.Then sketch the curves in the $x y$ -plane. $$r=1+\cos \theta$$

So we have the card. You he and by our egos one last time. So Well, we could have started figuring out What is, uh are for said I call zero. Well, zero she had played in that thing is going to want, like, kind of a deal. That's too. So what? The angles here would have already have two at this point because, uh, yeah, I was measuring respectful. Uh, e x axis is Donald zeros at that point, are you? Oh, by house, she'll be that I'm These are always perhaps Yeah. So perhaps, um um, just one plus cause I know how that is. He zeroes in just one. Yeah, that have something like these. When then, uh, the fight more than I get. We're on classical signs. Jeez, warn miners. One that is you. So your resume something that came on like these. So it's gonna be set up like these. Figure because, uh, where is coming to buy? It's slowly approaching two zeros off. Very. This is the question, because, well, one was signed off. We're always okay being, uh Well, this is one of his motor do, and it will be always bigger than you Because cause I know Vera, he's always the modern At mine is always bigger than my as one, uh, sort of it yet one to that equation. We get that on the well because, uh, because I know that people to sign off minus theater, you get precisely the same shaped by reflecting. We're there. See ya. It's a Mongol here. So young alpha, because you're dango. Now, mind her cell phone because you get for Don Igo here. We're gonna get some are how far these will be able to want last casino. My no cell phone. So there I should be the same. So, by that reason, uh, reflecting should give you the same shape. So should be in the sinker, so he's gonna have a seem a dream. What's your magic? We respect two. Reflection Thio The exception. True. No exceptions is because of these reasons. Because co sign off Ziegel took a sign of Maya's threat so that our awesome mind you he's gonna be the same off my nose. Dago. The same phrase. So what is this shit? Red Cheap

Our goal for this set of problems is to identify the graphs and sketch the curves. So if we have something like R equals two Plus sign data. And what we see is that this is our graph and then the symmetry would be y axis symmetry because we see there's a mirror image across the y axis but there isn't that across the X axis. Then we can look at some other examples Such as 1-plus 2 ST data. We do this again, we see it has this waxy symmetry. We're not X axis symmetry. Then we'll look at the sign of data over to and we get both X and y axis symmetry based on this, which means it also has origin symmetry. Next, we're going to consider co sign of theater over to and what we expect to find is similarly X and Y and X and Y. Symmetries as well as origin. Symmetries then we'll have are straight equals coast saying of Ceta. So that's gonna be the square root. This and not just the square root at the square root as well as the negative square root. So we can have both in and we'll see that it has this mere image. So this is symmetrical. It's effectively excellent access. We can also look at examples of women skates that's going to be the square root four. Co sign two theta. So it's a Lemonis gate example, this is going to have X and Y axis symmetry. And then we can also look at for of sine two theta. These are all individual examples. Again, we have this luminous gate, but this does not have X axis symmetry or waxes symmetry. It has symmetry with respect to the origin, however.

Our goal for this set of problems is to identify the graphs and sketch the curves. So if we have something like R equals two Plus sign data. And what we see is that this is our graph and then the symmetry would be y axis symmetry because we see there's a mirror image across the y axis but there isn't that across the X axis. Then we can look at some other examples Such as 1-plus 2 ST data. We do this again, we see it has this waxy symmetry. We're not X axis symmetry. Then we'll look at the sign of data over to and we get both X and y axis symmetry based on this, which means it also has origin symmetry. Next, we're going to consider co sign of theater over to and what we expect to find is similarly X and Y and X and Y. Symmetries as well as origin. Symmetries then we'll have are straight equals coast saying of Ceta. So that's gonna be the square root. This and not just the square root at the square root as well as the negative square root. So we can have both in and we'll see that it has this mere image. So this is symmetrical. It's effectively excellent access. We can also look at examples of women skates that's going to be the square root four. Co sign two theta. So it's a Lemonis gate example, this is going to have X and Y axis symmetry. And then we can also look at for of sine two theta. These are all individual examples. Again, we have this luminous gate, but this does not have X axis symmetry or waxes symmetry. It has symmetry with respect to the origin, however.

We want to sketch four points on a single set of coordinate axes, axes. So let's say that here is X. Here is why here, Z Then I'm going to denote the negatives and dotted lines. Just perhaps, it will make things clearer. Perhaps not so in the 1st 0.0 52 Let's call that a so zero long x five along why two loans e put a right there and second point called B for zero minus one. So four along X zero Long wait, Why minus one long Z's letters beam. See 246 Too long Eggs fora long. Why six along Z And finally, let's call the last point D one minus one, too. So when along X minus one along Why too long? See right there.


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