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Given the rectangular coordinates (2 , ~ 2v3) , which of the following polar coordinate pairs in (1 poit} radians represents the same point? 3 47 3 3 55If r + 0 , w...

Question

Given the rectangular coordinates (2 , ~ 2v3) , which of the following polar coordinate pairs in (1 poit} radians represents the same point? 3 47 3 3 55If r + 0 , which of the following polar coordinate pairs represents the same point as the point (2 points) with polar coordinates (r , 8) ? Select all that apply:(r,8-27) (r,8+T) 0 (-,8-7) (r,8 -37)Describe the position of the polar coordinatcs on the polar plane for (4,1209) . (1 point)on the fourth circlc from thc ccntcr and 1205 clockwisc fro

Given the rectangular coordinates (2 , ~ 2v3) , which of the following polar coordinate pairs in (1 poit} radians represents the same point? 3 47 3 3 55 If r + 0 , which of the following polar coordinate pairs represents the same point as the point (2 points) with polar coordinates (r , 8) ? Select all that apply: (r,8-27) (r,8+T) 0 (-,8-7) (r,8 -37) Describe the position of the polar coordinatcs on the polar plane for (4,1209) . (1 point) on the fourth circlc from thc ccntcr and 1205 clockwisc from thc horizontal axis on the fourth circlc from thc ccntcr and 609 countcrclockwisc from the horizontal axis on thc fourth circlc from thc ccntcr and 2409 clockwisc from the horizontal axis on thc fourth circlc from thc ccntcr and 600 clockwisc from thc horizontal axis



Answers

Find the rectangular coordinates for each point with the given polar coordinates. $(-1,7 \pi / 4)$

This point in polar to rectangular. Alright -5 or three. That's here. That's here. I don't know why through that that's 60 degrees so square 2321 that was negative X. Equals R. Co signed data, so that's negative six times one half Which is -3. And why equals R. Signed data, which is negative six times negative squared at 3/2, Which is positive three square roots of three, So -3, 3 squirts of three.

Rectangular four comma five pi over four. Okay. 12345 pi over four. That's 11 square to to because that's 45 degrees. Those are both negative. Um X. Is our coastline data Which is four times -1 over the square to to Which is -4 over the square to. I think I can fix that a little bit. That's minus four square roots of 2/2. So minus two square root 22. Why is our science theater? R is the same sign is the same. So my -2 squared of two, So -2 squirts of 2 -2 squirts of two.

Key. This problem gives us a Cartesian coordinate of negative for six, and it wants us to convert it till polar. Um and so I wrote over here right at the point saying we need to go to polar. But then when we do this, I kind of wrote look, a little, like review thing. Um, it's basically that triangle that we're making when we do it. Um, you go over x amount up. Why amount and that gives you a radius of are right. And Pythagorean theorem gives us X squared plus y squared equals R squared, since it makes a right triangle with data being that angle right there by the origin, right. So I square root did that to get our I'm gonna be using this equation, right? Because polar has an r and lips that's not honor our and then data. Hey, so I'm gonna be using that to get r. And then if you take the tangent of data, that's your opposite over your adjacent or your why over X and then whenever you want the angle used the ark or the inverse. So I'm gonna be using the inverse tangent toe. Find the data Okay, so those two equations are super important. And so now I just plug it in. Right? So r equals lips. Here we go. Our equals the square root of X squared. Need a four squared plus y squared, which is six word. And if you do that, that gives you the square root of 16 plus 36 which is the square root of 52. Now, I don't know if you have to do this by hand or using a calculator. Um, so I'm just gonna do it by hand. And if you have a calculator, great. Just type this in. Okay, But 52 let's simplify that. That's two times 26 right? So I broke that at 26 is too. And 13 broke that up. My friends go outside. So to route 13 and that is gonna be my are okay. And so I used that. And then now I need to find my feta. So I'm gonna use that inverse tangent function, and I'm gonna say that data is the tangent inverse ups tangent universe of and they used to Why, over x 06 over negative for okay. And what that gives me when you type that in. Okay, is I got negative. 56.309 ish. Okay, But you have to remember, Remember, houses consider the Quadra in which the point is located. Hey, no, I'm let me show you what that means per se. So we'll do blue negative for six means we go left for an up six. And that's my point. So right now we're in Quadrant two. Okay, Since we're in Quadrant two, this negative 56. What negative means I go, um, the opposite direction. So I'm gonna That really means I'm right here. That's the negative. 56.309 Well, I don't want that. I want to be in second quadrant here, So to get there, I need to add 180 degrees, so I'm gonna add ah, 180 to that. And when you do that, you get 123.69 degrees. OK? Cause that state you've gotta remember that quadrant. So when you put it all together, right, that means we use our our which is to root 13. And then you do 123.6 night because that's your data. So our data right there, that's your final answer.

So remember that X is equal to our co sign of data. And why is equal to our sign of data when we're trying to convert polar coordinates into rectangular coordinates. And so we have X is equal to a radius 8.1 times co sign of 5.2 radiance. And then we have why is equal to 8.1 times sign of 5.2 radiance and so and so calculating. This we get access is equal to 3.79 And why is equal to negative 7.16 negative. 7.16 And so putting this together, we have our coordinates 3.79 comma negative, 7.16 And so these are coordinates.


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