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3.6 Trigonometric Functions
Mon Oct 20
Do Now
Find the y’’ and y’’’
1)
2)
y = 2x + 5
y=x
1/ 2
HW Review: p.163 #1-29 37-45
Trig Derivatives
• Use the limit definition to find d/dx sinx
D/dx sin x and cos x
• Using the limit definition, the derivatives
are
d
dx
d
dx
sin x = cos x
cos x = -sin x
D/dx other trig functions
• Using the Quotient Rule, the other trig
derivatives can be derived:
tan x = sec x
d
dx
sec x = sec x tan x
cot x = -csc x
d
dx
csc x = -csc x cot x
d
dx
d
dx
2
2
Proof of one
• Pick a trig to prove
Ex
• Find the 9’th derivative of sin x
Ex 2
• Find the tangent line to the graph of
y = tanx secx at x = pi/4
Closure
• Find the 55th derivative of cos x
• HW: p.167 #1-45 odds
• 3.1-3.6 Quiz Wed
3.1-3.6 Review
Tues Oct 21
• Do Now
• Find the the derivative of each function
• 1) y = sinx cosx
• 2) y = x^2(tanx)
HW Review
3.1-3.6 Review
• Derivative Rules
– Power Rule, e^x
– Product / Quotient Rules
– 6 Trig Rules
• Derivative Applications
– Tangent Lines
– Rates of Change
– Higher Derivatives (Velocity, Acceleration)
Quiz
• 7 questions - 50 pts
• Derivative Rules
• Most questions are applications
– Tangent Lines
– Rates of change
Closure
• Of the 6 sections so far, which of the 6
seem most interesting? Why?
• Quiz tomorrow