# Thread: Converting Polar Equation to Rectangluar Equation

1. ## Converting Polar Equation to Rectangluar Equation

Okay, I need to convert r = 4 cos (theta) - 4 sin (theta) into a rectangular equation, and I'm stuck. My best guess is that I need to factor the 4 out of there and somehow square the sine and cosine to make it equal to 1, and that will give me my answer. Any help?

2. Originally Posted by JoshHJ
Okay, I need to convert r = 4 cos (theta) - 4 sin (theta) into a rectangular equation, and I'm stuck. My best guess is that I need to factor the 4 out of there and somehow square the sine and cosine to make it equal to 1, and that will give me my answer. Any help?
Multiply the entire equation through by r:

$r=4\cos\vartheta-4\sin\vartheta\implies r^2=4r\cos\vartheta-4r\sin\vartheta$

Take it from here. It shouldn't be much of a problem

--Chris

3. Originally Posted by JoshHJ
Okay, I need to convert r = 4 cos (theta) - 4 sin (theta) into a rectangular equation, and I'm stuck. My best guess is that I need to factor the 4 out of there and somehow square the sine and cosine to make it equal to 1, and that will give me my answer. Any help?
not necessary

multiply both sides of the equations by r. the required simplification should be staring you in the face from there. if not, say so

4. That was easier than I thought, heh. Thanks.