I too understand that a synchro is used to measure an angle of rotation. I'm only a simple mechanical guy at heart and am a bit confused by your reference to polar and cartesian co-ordinates. My understanding of these is that it goes beyond angular displacement and is now looking at distance moved from a central point. (i.e. we are looking at angle and distance or X and Y co-ordinates).
I've seen resolvers used in FADEC systems to provide power lever/thrust lever positional information. Other than that I can't help.
I look forward to learning a bit more from better qualified people than myself!
