Find the points of intersection of the graphs of the equations.r = 9(1 + sin(𝜃))r = 9(1 − sin(𝜃))r ≥ 0, 0 ≤ 𝜃 < 2𝜋

To find the points of intersection of the two polar equations, we need to set them equal to each other and solve for θ.

So, we have:

9(1 + sin(θ)) = 9(1 - sin(θ))

Solving this equation gives us:

1 + sin(θ) = 1 - sin(θ)

2sin(θ) = 0

sin(θ) = 0

The solutions to this equation in the interval 0 ≤ θ < 2π are θ = 0 and θ = π.

Now, we substitute these values into the original equations to find the corresponding r values.

For θ = 0:

r = 9(1 + sin(0)) = 9(1 + 0) = 9

r = 9(1 - sin(0)) = 9(1 - 0) = 9

So, one point of intersection is (9, 0).

For θ = π:

r = 9(1 + sin(π)) = 9(1 + 0) = 9

r = 9(1 - sin(π)) = 9(1 - 0) = 9

So, the other point of intersection is (9, π).

Therefore, the points of intersection of the graphs of the equations are (9, 0) and (9, π).