# Math Help - Polar Equation

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 $r=2\cos(\theta)$ since r is a function of the angle theta. The x and y coordinates can be found by the standard conversion:

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

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 $\theta$ instead of x?

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

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

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

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