1. ## Polar Equation

Convert the polar equation r=2cosx to rectangular coordinates and sketch the graph

2. Originally Posted by tiga killa
Convert the polar equation r=2cosx to rectangular coordinates and sketch the graph
r should be $\displaystyle r=2\cos(\theta)$ since r is a function of the angle theta. The x and y coordinates can be found by the standard conversion:

$\displaystyle x=r\cos(\theta)$
$\displaystyle y=r\sin(\theta)$

Look at this page for a nice explanation of common polar graphs. Yours should graph a circle.

Pauls Online Notes : Calculus II - Polar Coordinates

3. Originally Posted by tiga killa
Convert the polar equation r=2cosx to rectangular coordinates and sketch the graph
I assume you meant $\displaystyle \theta$ instead of x?

Multiply through by $\displaystyle r$ to get $\displaystyle r^2=2r\cos(\theta)$

We know that $\displaystyle r^2=x^2+y^2$ and that $\displaystyle x=r\cos(\theta)$ so our new equation is:

$\displaystyle x^2+y^2=2x \implies x^2-2x+1-1+y^2=0 \implies \boxed{(x-1)^2+y^2=1}$

So it's a circle of radius 1 centered at $\displaystyle (1,0)$.