pos is the progress ratio in the one_cycle going from 0 --> 1.
end-start: is the variation of the parameter which is then offset by start
Fx momentum starting at start=0.85, and maximum end=0.95
try this pesudo code
fx=[sched_cos(start=0.85, end=0.95, pos) for pos in range(0,1.01,0.01)]
import matplotlib as plt
plt.plot(fx)
For the answer of your first question, the warm restart happens because of the half wave, since the wave is halved, for the next oscillation it begins again from (end-start) instead of 0. That sudden shoot up is the warm up.