# Thread: Converting Polar to Rectangular Equations

1. ## Converting Polar to Rectangular Equations

Was curious if anyone new how to find an equivalant equation in cartesian coordinates for the problem r=2sin@+2cos@ I have to turn in my trigonometry final tomorrow and am having problems with this one. I also am not sure how to make a theta so @ is theta. thank you...

2. Originally Posted by Thalstead
Was curious if anyone new how to find an equivalant equation in cartesian coordinates for the problem r=2sin@+2cos@ I have to turn in my trigonometry final tomorrow and am having problems with this one. I also am not sure how to make a theta so @ is theta. thank you...
recall that $r^2 = x^2 + y^2$, also recall that, $x = r \cos \theta$ and $y = r \sin \theta$

so, start with $r = 2 \sin \theta + 2 \cos \theta$

multiply through by $r$,

$\Rightarrow r^2 = 2r \sin \theta + 2r \cos \theta$

Now what?

3. Originally Posted by Jhevon
recall that $r^2 = x^2 + y^2$, also recall that, $x = r \cos \theta$ and $y = r \sin \theta$

so, start with $r = 2 \sin \theta + 2 \cos \theta$

multiply through by $r$,

$\Rightarrow r^2 = 2r \sin \theta + 2r \cos \theta$

Now what?

The only next step that I can think would be to then have r^2=2y + 2x and possibly change the r^2 to x^2 + y^2

4. Originally Posted by Thalstead
The only next step that I can think would be to then have r^2=2y + 2x and possibly change the r^2 to x^2 + y^2
yes. we want to get rid of the r's and the theta's and get x's and y's, so that's exactly what we do. so we get x^2 + y^2 = 2x + 2y. but what kind of curve is that?

5. I'm not really sure.... I was looking through the chapters in the book and didn't find anything similar. It wouldn't be a polar graph because we replaced the r's and theta's

6. Originally Posted by Thalstead
I'm not really sure.... I was looking through the chapters in the book and didn't find anything similar. It wouldn't be a polar graph because we replaced the r's and theta's
of course it's not a polar graph anymore. it is a circle. now that you know that, could you say, find it's center and radius?

7. Oh I understand now! yes I know how to work with circles! thank you so much for you're help. I really appreciate it =)