A quest states:
In exercises 1-11, calculate div F and curl F for the given vector fields.
11. F = θ̂ (with a "hat" on top) = -sinθi + cosθj.
If I rewrite F in terms of cartesian coordinates I get:
-(y/(√(x2 + y2)) + (x/√(x2 + y2))
Then by differentiation followed up by addition as the devergence theorem says I get anything but 0, which is the correct result for this task. How come? Have I not converted the polar coordinates into cartesian coordinates correctly? If I can solve this problem, finding the curl of F shouldn't be that hard.