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 9 months ago
Convert the polar equation to rectangular form and identify the graph.
r= 7/ (2cosΘ+5sinΘ)
 9 months ago
Convert the polar equation to rectangular form and identify the graph. r= 7/ (2cosΘ+5sinΘ)

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music101
 9 months ago
Best ResponseYou've already chosen the best response.0dw:1393722700861:dw

sourwing
 9 months ago
Best ResponseYou've already chosen the best response.0y = r sin(theta) x = r cos(theta) x^2 + y^2 = r^2 plug and chug

music101
 9 months ago
Best ResponseYou've already chosen the best response.0yea so how would i plug it in

music101
 9 months ago
Best ResponseYou've already chosen the best response.0cuz i did this last week and i kinda forgot sorry

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1Try getting your cos and sin with r over there by multiplying both sides by 2cos(theta)+5sin(theta)

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1So you have: \[2rcos(\theta)+5rsin(\theta)=7 ?\]

music101
 9 months ago
Best ResponseYou've already chosen the best response.0why would you put r w/ each one of the terms isnt there just 1?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1\[r=\frac{7}{2\cos(\theta)+5 \sin(\theta)} => r(2\cos(\theta)+5 \sin(\theta))=7\] Distributive property!

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1you should have it from here. Use the equations sour gave you.

music101
 9 months ago
Best ResponseYou've already chosen the best response.0what if the question's like r= 3sinΘ ?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1Try multiplying r on both sides recall rsin(theta)=y and r^2=x^2+y^2

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1right so now you are able to replace rsin(theta) with y and r^2 with x^2+y^2

music101
 9 months ago
Best ResponseYou've already chosen the best response.0the square root of that right?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1just do exactly what I said replace r sin(theta) with y replace r^2 with x^2+y^2

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1you are done what else do you want?

music101
 9 months ago
Best ResponseYou've already chosen the best response.0is tht my final answer

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1putting an equation in terms of just x and y ( or just x or just y) is called a cartesian equation if that was the directions to just right as a cartesian equation then you are done

music101
 9 months ago
Best ResponseYou've already chosen the best response.0right, sorry. i missed a problem on my homework it was r= 2sinΘ4cosΘ

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1multiply both sides by r

music101
 9 months ago
Best ResponseYou've already chosen the best response.0do you square both sides 1st

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1replace r^2 with x^2+y^2 replace r sin(theta) with y replace r cos(theta) with x

music101
 9 months ago
Best ResponseYou've already chosen the best response.0ok i did that: x^2+y^2= 2y4x

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1yep. :) that is right you wrote the poloar equation as a cartesian equation if that is all the directions said to do then you are done.

music101
 9 months ago
Best ResponseYou've already chosen the best response.0aand i missed r= 3+3cosΘ

music101
 9 months ago
Best ResponseYou've already chosen the best response.0so i multiplied both sides by r 1st

music101
 9 months ago
Best ResponseYou've already chosen the best response.0and got x^2+y^2=3r +3x but dont i need to get rid of the r?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1you could subtract both sides by 3x giving you \[x^2+y^23x=3r \] then square both sides and replace the r^2 with x^2+y^2

music101
 9 months ago
Best ResponseYou've already chosen the best response.0why square both sides?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1I just prefer my answer without radicals and me squaring both sides will allow me to write my answer without radicals

music101
 9 months ago
Best ResponseYou've already chosen the best response.0so what would be final answer then

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1what if you with what I was saying take my equation and then square both sides and then replace the r^2 with x^2+y^2 you will have your final answer

music101
 9 months ago
Best ResponseYou've already chosen the best response.0yeah but when you square the whole left side you get x^4+y^49x^2 = 3x^2+y^2?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1\[(x^2+y^23x)^2=(3r)^2 \] the us what you get when you square both sides your equation is not equivalent to that you squared each term sorta but not really it is whatever you do to one side of equation you can do to the other and the equation still holds

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1\[\text {recall law of exponents} (3r)^2=3^2r^2=9r^2=9(x^2+y^2) \]

music101
 9 months ago
Best ResponseYou've already chosen the best response.0im not following are you saying keep left side just squared in parentheses?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1It is easier than multiplying it out, don't you think?

music101
 9 months ago
Best ResponseYou've already chosen the best response.0yes. so only change right side. like substitue

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1You can multiply it out if you want. Just do it correctly, but the if the directions just say write as a rectangular (aka cartesian equation) than you are done. If the left hand side was already in terms of x and y. r^2 was the only thing that needed to be converted.
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