Find the points of intersection of the graphs of the equations. (Enter (0, 0) for the pole.)r = 𝜃3r = 3

The given equations are in polar coordinates. The first equation is r = 𝜃/3 and the second equation is r = 3.

To find the points of intersection, we set the two equations equal to each other and solve for 𝜃:

𝜃/3 = 3 𝜃 = 9

Substitute 𝜃 = 9 into the first equation to find r:

r = 9/3 = 3

So, the point of intersection in polar coordinates is (r, 𝜃) = (3, 9).

However, the question asks for the intersection points in Cartesian coordinates. To convert from polar to Cartesian coordinates, we use the formulas x = rcos𝜃 and y = rsin𝜃.

Substituting r = 3 and 𝜃 = 9 into these formulas, we get:

x = 3cos(9) y = 3sin(9)

So, the point of intersection in Cartesian coordinates is approximately (x, y) = (-1.879, -0.684).