So, I search for the definition of cycle and I get this in Wikipedia:
A turn is a unit of angle measurement equal to 360° or 2π radians (or ...). A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot.
When I look for motion in pendulum, I get:-
The time for one complete cycle, a left swing and a right swing, is called the period.
So, in the first quote, it says that one cycle has to be 2π radians, but in the second quote it says "one complete cycle" is "a left swing and a right swing" (i.e the full cycle doesn't have to be equal to "2π radians").
Can you please clarify what I see as contradicting statements?