Answer
$(x-1/2)^2 + y^2 = 1/4$
See graph below.
Work Step by Step
The question asks for a graph of the polar equation and to convert the equation into rectangular coordinates
Given $r = \cos θ$
Table of Values:
$(1, 0)$
$(0.5, \frac{\pi}{3})$
$(0, \frac{\pi}{2})$
$(-0.5, \frac{2\pi}{3})$
$(-1, \pi)$
$(-0.5, \frac{4\pi}{3})$
$(0, \frac{3\pi}{2})$
$(0.5, \frac{5\pi}{3})$
See graph below.
To convert the equation into rectangular coordinates, the following equation can be used:
$r^2 = x^2 + y^2$ $x = r \cos θ$
So $r = \cos θ$
$r^2 = r \cos θ$
$x^2 + y^2 = x$
$x^2 - x + y^2 = 0$
$x^2 - x + 1/4 + y^2= 0 + 1/4$
$(x-1/2)^2 + y^2 = 1/4$
Circle centered at (1/2, 0) with radius 1/2
