Find an equivalent equation in polar coordinates: 2x + 3y = 6?

Question

A) 2 cos theta + 3 sin theta = 6r
B) r(2cos theta + 3 sin theta) = 6
C) 2 sin theta + 3 cos theta = 6r
D) r(2sin theta + 3 cos theta) = 6

Answer 1

y = r sin theta, x = r cos theta (by drawing a triangle or otherwise.)
Substitute them in:
2r cos theta + 3r sin theta = 6.
Or r(2 cos theta + 3 sin theta) = 6.