# Converting Polar Equation to Rectangluar Equation

• Sep 14th 2008, 06:10 PM
JoshHJ
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?
• Sep 14th 2008, 06:12 PM
Chris L T521
Quote:

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 :D

--Chris
• Sep 14th 2008, 06:12 PM
Jhevon
Quote:

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
• Sep 14th 2008, 06:22 PM
JoshHJ
That was easier than I thought, heh. Thanks.