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Find an equation for the given polar graph: [Note: Numeric labels on these graphs represent distances to the - origin ] 10 (b) 15|Four petal roseLimacon(a)io) =Edit...

Question

Find an equation for the given polar graph: [Note: Numeric labels on these graphs represent distances to the - origin ] 10 (b) 15|Four petal roseLimacon(a)io) =Edit(b) 7(0) =Edit

Find an equation for the given polar graph: [Note: Numeric labels on these graphs represent distances to the - origin ] 10 (b) 15| Four petal rose Limacon (a)io) = Edit (b) 7(0) = Edit



Answers

Find an equation for the given polar graph. [Note: Numeric labels on these graphs represent distances to the origin.] (Graph cannot copy)

So for the script here. First we want to just get a circle, and it's clear that we have a radius of five. So that's a pretty basic graph that's just gonna be R equals I've which is just a circle with Radius five centered at the origin. Pretty basic example. Then we want to show another circle. The only thing that's different, though, is we want it to be offset instead. We wanted to be centered such that, um, it's intercept is at six. Which clearly means that the value has to be different. So since the center is on the X axis, um, and we see that data is going to be equal to pi over two. We end up getting that this is going to be our equals six coast on data I'm in. The six helps us realize that when the coastline is equal to, um, Pi over two will get zero when coastline is equal to zero will get to six. That's how we are able to determine that. And then lastly, we want a cardio rdgraf. Um so we see that with this graph we want two years co sign, but we wanted to be zero at zero and, um, native to So how we're going to write this is R equals one minus crossing data. Because when we do this, since, uh, the graph intersects at data being equal to pi over two, we see when it's pi over two, we wanted to be zero. And then, um at pie is well, we wanted to be zero. So that's how we end up getting this graph right here.

For this graph. We are trying to get a four pedal rose, and we see that one of the points that it reaches is three at the tip. So based on what we know regarding our our properties of these graphs, eso the four pedal rose is going to be characterized by sign of Greek feta. But that's where just equals one right here at this point. Instead, we wanted to equal a three. So to do that, we're just gonna multiply this by three, and then we get the four pedal rose that we're looking for. Then we want a Loomis or cardio oid shaped graph. Um, And to do that, we're gonna r equals. It shifted down what appears to be a few units, so it's shifted them. Three units will have a minus three, and then we're going to add e cardio graft shape so it could be too sign data. So we see that the negative three plays a role in the fact that that determines, um, where when we do the negative and result in the intercepts being here and here and then the to sign data will increase the magnitude of it. Um, and then the sign graph ensures this cardio I'd shape then. Lastly, we have, um, 11 escape, which looks so much an infinity sign eso How this one works is it's going to be our equals. And then since it reaches three, we're going to do three with London State. We have to use the square root. I mean, it's it's from the book. It's going to be a co sign in this case is gonna be coastline of two theta. Okay, because it has that double pedal look to it. So you see that this is our women escape graph.

So for this problem, number 20 we, uh it's important to be able to switch between polar graphs and other graphs. And in this case, what we have here is we have the equation of a polar graph and ultimately, what we're trying to do with it for problem 20 is we want to create this polar graph, given the equation that we have. So starting off, what we're going to have is this cardio I'd shape. We know that the cardio shape since it intersects with three is going to be our equals. Three. I'm going in. This case is going to be a minus graph. I mean, it'll be minus three sign Fada. So we see that's what we wanted. Three ensures that it intersects with the three and then minus three ensures that it's facing this downward direction. And then, um d three also, uh, controls the how large the cardio and graph is. Then what we have next is going to be a five pedal rose. So if he's we're gonna have our equals. And since the A value is one, it doesn't go beyond that. We're just gonna have one Times co sign of five Fada. The reason why we know it's coastline is because the graph intersect at the X axis on the X value is oftentimes very much connected to the idea of the coastline graph. Then lastly, we have way, have a circle. And with this circle in particular, um, it's above the X axis. Um, it's touching the Y axis at four. So what that's going to give us is we have our Equalling for sign. Fada on this ensures that the graph intersects it for like so.

So let's start looking at these different graphs that we have available first. It's just gonna be the plane circle with its center at the origin and radius of five. So that's just gonna be R equals five, simple enough. Then we have it off centered. So this is going to be um three co signed data For a 6% data. Where the are is the or this is the radius right here. six. And then the coastline data indicates that we are going to be um that we're going to be at the along the X axis in the positive direction. If this was a negative 6% data would be on the other side. If this was signed beta, then it would be up on the Y axis. If it was negative sign data, it would be below on the y axis. So that's how we determine this. We could also put this more in rectangular form, but this is the simplest way to do it. If we're familiar with these kinds of equations.


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