Find the point(s) of intersection for the polar curves with equations r = 6 cos θ and r = 4 − 2 cos θ

Question

Find the point(s) of intersection for the polar curves with equations r = 6 cos θ and r = 4 − 2 cos θ

A
B
C
D	0, π

Answer 1

When we want to find points of intersection of any two functions, we just set them equal. In this case, we want 6 cos t = 4 - 2 cos t

If we move all of the cos t terms over to the right, we get that 0 = 4 - 8 cos t. This means that 8 cos t = 4, so cos t = 1/2.

Since cos (π/3) = 1/2 and cos (-π/3) = 1/2, these are both points of intersection for the polar curves we are given.