Your is already in terms of and , so you just need to convert and to Cartesian coordinates. So .
F(r,θ) = ri + sinθj, where (r,θ) are polar coordinates in the plane.
In my book are given both formulas to calculate div F and curl F - but only for cartesian coordinates. What counts for polar coordinates in the plane? It is like I am to differentiate ri with respect to x and sinθj with respect to y: Am I wrong to think so?
div F equals cos θ (1 + (1/r) cos θ)
If I take the derivative of i with respect to x and plus it with the derivative j with respect to y I don't get this answer above (taken from the book).
Best regards Kaemper