Hm...

I guess I'm just confused on how to use GT in this context. Is there a vector field given? If not do we just assume the vector field is just <0,0,0>? If so, Green's Theorem would just simplify to finding the area of a region using a double integral. If this is the case, you should evaluate the double integral in polar coordinates. So, you will have $\displaystyle \int_0^\frac{\pi}{16}\int_0^{13sin(16\theta)}rdrd\ theta$.

This is the only thing I can figure out. I got the r limits from the equation given, and the theta limits by graphing in polar coords on my calculator. If you set your $\displaystyle \theta$ step to $\displaystyle \frac{\pi}{256}$, $\displaystyle \theta$min to 0 and $\displaystyle \theta$max to $\displaystyle \frac{\pi}{16}$ then you will see exactly one petal of that function.

This seems to be the only way to do it to me. Like I said, I'm not sure why they ask you to use GT...there might be something I'm missing. Hope this helps