I was coaching a student on how to approach this problem. 2 equations given and the question was where they intersect.
Now, with a bit of practice on polar coordinates, producing the graph by hand wasn't too tough. I was able to point out the petal in the first quadrant wan't going to intersect the vertical line unless rotated 30 degrees clockwise.
The student said the result was expected to be algebraic, i.e. set the 2 equal, manipulate and show no solution. I wasn't able to do this after about 10 minutes of manipulation, I just would up with sine to the 3rd power along with a number of sine*cos terms.
I'm not so much looking for this single solution as I am a process how to approach this style of problem. (This is for a pre-calc class, typically with high school juniors)