There are 60 complete cycles per second. A cycle is one complete 360 degree rotation, starting a zero, going maximum positive @ 90 degrees, back to zero at 180 degrees, maximum negative @ 270 degrees, and back to zero where it started @ 360 degrees.
Of the 60 cycles in a second there are 60 maximum positive peaks and 60 maximum negative peaks every second.
If you have only one diode in series with the secondary of a transformer (transformer for isolation from the power main) you will see 60 peaks per second because the diode only conducts in one direction. Depending on the direction the diode is wired in, the peaks may be positive or negative, but not both unless the diode shorts.
You would see the cycle start at zero, reach a maximum @ 90 degrees, return to zero @ 180 degrees, and stay there through 270 degrees on to it's return to zero, for a total of 60 half waves, hence a half wave rectifier.
A full wave configuration catches both positive and negative peaks using either 4 diodes in a bridge configuration or 2 diodes with a center tapped transformer. With a full wave rectifier you will see both the positive peak @ 90 degrees, and a positive mirror image of the negative peak @ 270 degrees for 120 peaks per second because there are 2 peaks per cycle.
My no name MIG machine uses a center tapped transformer and a full wave configuration.
Hope this helps clarify.
Best regards to all, steve