Fact 3: a [sin 0] = cos 0 "the derivative of sine is cosine" To prove Fact 3 (that [sin 0] = cos 0) and Fact 4 (that [cos 0] = - sin 0) we must prove the following facts: Fact 4: [cos 0] = - sin 0 "the derivative of cosine is the opposite of sine" Fact 1: sin 0 - = 1 Problem 1 Find the derivative of Y(x) = (1 - cosx)/(1 + sin x) Fact 2: 1 - cos 0 lim = 0 We will do this in class. Problem 2: Find the derivative of sec 0 using the Quotient Rule and Facts 3 and 4