# Thread: intersecting points - polar coordinates

1. ## intersecting points - polar coordinates

Hi

C1 r= 3cos x
C2 r= 1 + cos x

First question is find the polar coordinates of the intersection points of the two curves.

I have found (3/2, pi/3) and (3/2, -pi/3) now what I am wondering is the point that we would normally consider (0,0) also an intersecting point and how would I find the coordinates for this point?

Thanks

Calculus beginner

2. Originally Posted by calcbeg
Hi

C1 r= 3cos x
C2 r= 1 + cos x

First question is find the polar coordinates of the intersection points of the two curves.

I have found (3/2, pi/3) and (3/2, -pi/3) now what I am wondering is the point that we would normally consider (0,0) also an intersecting point and how would I find the coordinates for this point?

Thanks

Calculus beginner
Your question seems to be a bit unclear. (0, 0) is not in the solution set. In fact neither of your given curves passes through this point. As to the rest we have
$r = 3~cos( \theta)$
and
$r = 1 + cos( \theta)$

Since r = r this means
$3~cos( \theta) = 1 + cos( \theta)$

so
$2~cos( \theta) = 1$

$cos( \theta ) = \frac{1}{2}$

You have mentioned the only two correct solutions. ( pi / 3 is the reference angle so there is another solution 4 pi / 3, or -pi / 3 which you already gave.

-Dan