## 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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1. JoannaBlackwelder

I think you will need these equations for the first one:|dw:1433136389230:dw|

2. JoannaBlackwelder

Any ideas how to use those?

3. anonymous

Sort of I plug r into the equations, no? so 6(cos)(theta)

4. JoannaBlackwelder

Well, I think it is easier to start with the bottom equation.

5. JoannaBlackwelder

|dw:1433136768548:dw|

6. JoannaBlackwelder

Do you see how I solved for costheta?

7. anonymous

OH

8. anonymous

Okay wait, but doesn't the botto equation just give you x/6 =costheta?

9. anonymous

how do I find x?

10. Michele_Laino

hint: 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: $\Large \sqrt {{x^2} + {y^2}} = 6$

11. Michele_Laino

please square both sides of that equation, what do you get?

12. JoannaBlackwelder

Yes, the bottom equation gives x/6=costheta, which makes cos^2theta = x^2/6^2

13. JoannaBlackwelder

|dw:1433173120794:dw|

14. JoannaBlackwelder

Can you do a similar process with y=rsintheta?

15. anonymous

@JoannaBlackwelder To answer your first question you get $x^2+y^2=36$

16. anonymous

Or that was Michele's.

17. anonymous

Oh it's a circle with a radius of 6.

18. JoannaBlackwelder

Yep :-)