Sketch the graphs of the polar equations r^2 = 9sin(2theta) and r = 2...?

Question

I also need to find 4 points of intersection and "Show work."
I can easily graph those two in polars, although I'm not positive how to show work while finding intersecting points.

(Keep in mind I'm not in Calculus...so if you have a way with derivatives/integrals...I can't do it :p)

Answer 1

Put r = 2 into the first equation, we have:
4/9 = sin(2theta)
thus: 2 theta = 2*k*pi + arc sin(4/9), and
2 theta = (2k+1)pi - arc sin(4/9)
where k = 0, and 1.
These are your 4 points of intersection (with same r and different theta's).
The graph looks like a two-leaf rose-patel (with symmetric axis Theta = pi/4) intersecting with a circle at origin with radius r = 2.

Answer 2

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