Let me startover what I am saying is there is only one 60 hz signal
across the center tapped transformer. Both leads are the same signal
the and do switch polarity 180 degrees at the same time. When you
reference to the neutral and check both with an oscilloscope you see
that the peaks and valleys match on the sine wave adding the together
you get the full 240v.

My problem has been in the description creating an image in my mind of
two sine waves out of phase with each other.

The potential of both of the hot leads oscillates at the same time and
are always 180 degrees apart on the sine wave.

So in the end it was how I interperted what was being said and
creating an image of what was being said as not fully correct in my
head.

Does that make any sense?

Mark