Find the polar equation of each of the given rectangular equations.$$x=3$$...

Rectangular Equations to Polar Equations Convert the equation to polar form.
$x=4$

This is problem 52 section 8.1 and we're tasked with finding this polar equation into rectangular coordinates on DSO. If you remember, the equation R squared equals at squared plus y squared we're actually gonna plug in, are here to find the wrecking the equation so R squared. So this is gonna be negative. Three squared is equal to x squared plus y squared and we'll go ahead and square that. So that's gonna be nine is equal to X squared plus y squared. And so now we've converted our polar equation and directing you like hornets.

So this is problem 60 section 8.1 on were asked to convert the polar equation here into rectangular coordinates. And so the first thing we'll do is we'll go ahead and distribute the three. So our is equal to, um three minus three. Sign data on we're gonna multiply both sides by R to make things a little bit easier for us. So multiply are multiplied by our and so this is gonna be our squared is equal to three are minus three r sine data on. And if you remember the equation, why is equal to our sign of feta? Um, we can actually substitute that here. So this is gonna be, uh, sorry. R squared sequel to three are minus three. Why? Um, and then we're gonna go ahead and use. The equations are squared, equals X squared, plus y squared. And so the reason why we're doing that. Israel, go ahead and set this side ableto x squared. Plus y squared is equal to three are minus three. Why? And now we can add three wine, both sides. And so then we're going to get X squared plus y squared. Plus three. Why is equal to three are and we're going to go ahead and square. Both sides squared, squared, and so this is going to be equal to X squared plus y squared plus three. Why square is equal to nine r squared. Um, and we can go ahead and use this equation here once more. This equation here to plug in for R squared so would get X squared plus y squared plus three. One square is equal to nine times x squared plus y squared. And so we went ahead and converted our polar equation in directing their coordinates.

Hey, this problem wants us to convert X equals three the, um, Cartesian equation to a polar one. And so I wrote this equation. Read that X equals arc. Oh, Sang Dita. Um and so all we have to do is plug that in. So since we do this, we say X is our co sign. Data is equal to three. Okay. And now, to get a polar equation we just saw for her. So I'm gonna divide coastline data from each side grain that it turns to a one. And so I get are equals three over coastline data, okay. And so you can leave it like that, or you can recognize that that's the same is three times one over coastline data and then Kwan over coastline data is really just the sea can write. It's the reciprocal. And so I can write that as three as this is three c camp data, okay. And that's almost prefer it. They don't like fractions if you don't have to have them. So I just rewrote it as c can't. But it is the same as that one right there. And that's how you do. It came

For this question, we have X is equal to zero. And why is equal to negative square root of three Find the radius we have really squared is equal to X squared plus y squared x zero. In this case, why's negative? Radical? Three. So are our square is equal to the positive three. And because we want a radiant ladies to be positive, it's gonna be the positive radical. Three. As for the angle, I know that wise equals R 10 to sign of data. So our sign of data, that's why divided by R, which is just negative, radical three over radical three, which is just equal to negative one so that our data okay, it's gonna be equal to the AARP sign one which it's just gonna be three by half. So her pork are points. Dependable importance is equal to our religious three. They're angle just 35 That's your answer