# 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...

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