Green's theorem applied to polar graph

csnsc14320

1. The problem statement, all variables and given/known data

Use Green's theorem to compute the area of one petal of the 28-leafed rose defined by [tex]r = 5sin(14 \theta)[/tex]
2. Relevant equations
[tex] A = \frac{1}{2} \int_c{x dy - y dx}[/tex]
[tex]\int \int_c{M_x + N_y}dx dy[/tex]


3. The attempt at a solution

I'm really more confused about just what to do outright. Green's theorem tells me that I can take the integral in that area formula and compute the double integral of the divergence of a vector field F = <M(x,y),N(x,y)>, but I have no idea how that helps me since I don't see any vector field here and I don't know the components N and M.

I think maybe I need to turn the expression [tex]r = 5sin(14 \theta)[/tex] into cartesian coordinates, but not really seeing what to do from here.

theres just too many equalities in greens theorem >:(

tiny-tim

Hi csnsc14320!

(your equations look a bit odd)

Hint: you're looking for a function whose curl is constant.