It would appear that the
Disk function, when asked to produce the sector of an ellipse between two angles treats those angles as Eccentric Anomalies (i.e. arguments to a parametric plot) rather than true central angles (i.e. arguments to a polar plot). The first part of my question asks whether this observation is correct?
Given that I want to construct a sector using the true central angles, I know that I can make use of the polar equation
(r=(a*b)/Sqrt[(b Cos[θ])^2+(a Sin[θ])^2];), but this does not provide me
Disk's ability to color the resultant sector. So, the second part of my question is, does Mathematica provide me a function for performing this filling operation?