The Unit Circle and Trignomoetric Functions
Use the Sum Formula for Cosine to derive the following identity for the average rate of change of the cosine function:
cos (x + h) − cos x /h = cos x (cos h − 1)/h − sin x (sin h)/h
Note: You will learn in Calculus 1 that limh→0(cos h−1)/h = 0 and that limh→0 sin h/h = 1. It follows that the instantaneous rate of change of cos x is − sin x.