3. Plotting Polar Coordinates

Plot the graph of $r = 2\cos(\theta)$

Lets write the table for this using increments of $\dfrac{\pi}{6}$

$\theta$	$0$	$\dfrac{\pi}{6}$	$\dfrac{\pi}{3}$	$\dfrac{\pi}{2}$	$\dfrac{2\pi}{3}$	$\dfrac{5\pi}{6}$	$\pi$	$\dfrac{7\pi}{6}$	$\dfrac{4\pi}{3}$	$\dfrac{3\pi}{2}$	$\dfrac{5\pi}{3}$	$\dfrac{11\pi}{6}$	$2\pi$
$r=2\cos\theta$	$2$	$\sqrt{3}$	$1$	$0$	$-1$	$-\sqrt{3}$	$-2$	$-\sqrt{3}$	$-1$	$0$	$1$	$\sqrt{3}$	$2$

plotting this we can see we get a circle

r = 2\cos(\theta)

multiple both sides by $r$

r^2 = 2r\cos(\theta)

sub in $r^2 = \sqrt{x^2 + y^2}$

x^2 + y^2 = 2x

rearrange

x^2 - 2x + y^2 = 0

simplify

(x - 1)^2 - 1 + y^2 = 0

which comes to

(x - 1)^2 + y^2 = 1

hence $r = 2\cos(\theta)$ is a circle with radius $1$