Derivative of sin(x), CAREFUL PROOF | Tricky Parts of Calculus, Ep. 1

I prove that the derivative of sin(x) is cos(x), with attention to key difficulties usually ignored in a calculus class. I focus on the significance of the choice of definition of the trig functions in terms of arc-length parametrization of the circle. In some presentations, the trig functions may be defined differently to make computing the derivative easier at the expense of having to develop much more theory and having to introduce a definition no one would have come up with in the first place! This is Episode 1 in a series of videos explaining the subtle points of calculus that are usually glossed over in a calculus class. Next video on the work of Archimedes on the circle to complete the proof that the limit as x goes to 0 of sin x /x is 1:    • Sin(x), x, tan(x) inequalities and Archime...