**Convert r=2costheta to rectangular equation**

**Answer:**

Multiply both sides by r, so you get r^2=2rcos(theta). Since X=rcos(theta) and r^2=x^2+y^2, you can rewrite the equation as x^2+y^2=2x. Now just rearrange everything, so x^2-2x+y^2=0. Then you can get (X-1)^2+y^2=1 as your final answer.