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October 29, 2013 3.5 Derivatives of Trigonometric Functions M E M O R I Z E y = sin x y' = cos x y = cos x y' = -sin x y = tan x y' = sec2x y = sec x y' = sec x tan x y = csc x y' = -csc x cot x y = cot x y' = -csc2x Find y' Ex 1) y = sin x - tan x + 5x Ex 2) y = x csc x Pythagorean Identities Find y' Ex 3) y = sin x + cos x cos x Ex 6) Review of Unit Circle Ex 9) csc 11π 6 tan 5π 4 cot 7π 4 sec 7π 6 October 29, 2013 Find the derivative of each. 3.5 Derivatives of Trigonometric Functions Day 2 y = sin x y' = cos x y = cos x y' = -sin x y = tan x y' = sec2x y = sec x y' = sec x tan x y = csc x y' = -csc x cot x y = cot x y' = -csc2x Ex 2) y = csc x Ex 3) Which of the following is an equation of the normal line to y = sin x + cos x at x = π? Find y' Ex 4) y = Ex 1) y = sec x cos x 1 + sin x Ex 4) Find y'' if y = x sin x A. -x sin x B. x cos x + sin x C. -x sin x + 2 cos x D. x sin x E. -sin x + cos x A. y = -x + π - 1 B. y = x - π - 1 C. y = x - π + 1 D. y = x + π + 1 E. y = x + π - 1 Ex 5) A body is moving in simple harmonic motion with position s = 3 + sin t. At which of the following times is the velocity zero? A. t = 0 B. t = π/4 C. t = π/2 D. t = π E. none of these October 29, 2013 Ex 5) Write an equation for the tangent line and normal line to graph y = x + cos x at (0,1)