The reason radians are used is because the derivative of sin(x) is directly cos(x) when using radians. This is why the formulations using radians come out cleaner.
I would like to add too that you very rarely get 90 degrees in a circuit. The parasitic effects will cause the angle to be all over the map, positive and negative, the extent of which is dependent on the frequency of the signal.
Simply-q: Break-in effects are largely due to parasitic capacitance effects through the air, insulation, cable sheaths, PC boards, etc., surrounding the signal-carrying wire(s). The capacitance is formed between the wire and "ground," which can be just about anything at a lower potential, and everything in between ground and the signal is the dielectric. These effects are part of what I was talking about. The fact the ground is indeterminate is what leads to the mystery of break-in. As time goes on, the more-dominant capacitances charge to a "neutral" level and finally break-in "ends." This is in addition to any physical material changes due to heat or an applied field.
There has been extensive research done by the French government (and the Germans to a certain extent) on this effect as it relates to high-power transmission lines. It is easier to witness when you're dealing with MV instead of mV. (When you stand under a power line, you are quite literally standing inside a capacitor.) They have shown that just the heavy ions in air can have a big impact on the capacitive resonance effects that affect a signal. But they are far from nailing down all the variables in all instances, of course.
Arthur
