the first coil's output begins at zero degrees and reaches 115V at 90 degrees
Thanks for the excellent posts everybody.
There is one small point that I have not noticed mentioned so far.
I now cannot recall the details (but there for sure will be someone along in a minute who does) but the peak voltage is not 115.
The voltages quoted are as I recall so called Root Mean Square (RMS) values. I think that they are used because they make V=IR work for sinusoidal AC in exactly the same manner that it does for DC.
In the UK our single phase voltage (household) is 240 volts (ish - it may have been reduced a bit) and the three phase voltage (available for business use on request - never used domestically) is 440V. Both RMS. The peaks are much higher. (On recall, from decades ago, it might be square root of 2 times higher [1.41])