Today, I ran into a calculus class and the professor was calculating the perimeter of a circle using arc lenghts. Even though they seemed to be on the right track, there is a problem:
They are using sinx and cosx functions, which are actually defined using the perimeter of a circle, aren't they? So, in my opinion, that was not a real proof since they were using what they want to show.
Or am I missing something? Was that a real proof?
Edit: I don't know but most probably they defined sinx and cosx in the usual way, because it was a calculus class.