Download 3.5 Derivatives with trig functions

October 29, 2013
3.5 Derivatives of Trigonometric Functions
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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)