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anonymous
 one year ago
Transform each polar equation to an equation in rectangular coordinates and identify its shape.
r = 6
r = 2cosθ
anonymous
 one year ago
Transform each polar equation to an equation in rectangular coordinates and identify its shape. r = 6 r = 2cosθ

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JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0I think you will need these equations for the first one:dw:1433136389230:dw

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Any ideas how to use those?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sort of I plug r into the equations, no? so 6(cos)(theta)

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Well, I think it is easier to start with the bottom equation.

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433136768548:dw

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Do you see how I solved for costheta?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay wait, but doesn't the botto equation just give you x/6 =costheta?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: since the subsequent transformation equations holds: \[\Large \left\{ \begin{gathered} x = r\cos \theta \hfill \\ y = r\sin \theta \hfill \\ \end{gathered} \right.\] then we can write: \[\Large \sqrt {{x^2} + {y^2}} = r\] Now, substituting into your first equation, namely r=6, we get: \[\Large \sqrt {{x^2} + {y^2}} = 6\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0please square both sides of that equation, what do you get?

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Yes, the bottom equation gives x/6=costheta, which makes cos^2theta = x^2/6^2

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433173120794:dw

JoannaBlackwelder
 one year ago
Best ResponseYou've already chosen the best response.0Can you do a similar process with y=rsintheta?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@JoannaBlackwelder To answer your first question you get \[x^2+y^2=36\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Or that was Michele's.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh it's a circle with a radius of 6.
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