Find the points of intersection of the graphs r = 3 - 3cosx and r = 3cosx

Answer 1

To find where the values equal each other r=r, set them equal to each other:

3 - 3cos(x) = 3cos(x)

1 - cost(x) = cos(x) - by multiplying both sides of equation by 1/3

1 = 2 cos(x) - by adding cos(x) to both sides of equation.

1/2 = cost(x) - by dividing both sides of equation by 2.

This occurs at either pi/3 or -pi/3 or any 2pix either of those.

Answer 2

Just need to equate the two equations and solve for the angle to get the point(s) of intersection.

3-3cos(x) = 3cos(x)

6cos(x) = 3

cos(x) = 1/2

x = arccos(1/2) = π/3 + 2πk and 5π/3 + 2πk.