1. Chapter 3 – Differentiation Rules
3.3 Derivatives of Trig Functions
Section 3.3 Derivatives of Trig Functions
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2. Section 3.3 Derivatives of Trig Functions
Remember…
*This functions represents the inverse sin of x (arcsinx) and not any of the other listed functions.
Section 3.3 Derivatives of Trig Functions
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3. Section 3.3 Derivatives of Trig Functions
Definitions
Section 3.3 Derivatives of Trig Functions
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4. Section 3.3 Derivatives of Trig Functions
Derivative: Sine
If we sketch the graph of the function f (x) = sin x and use the interpretation of f (x) as the slope of the tangent to the sine curve in order to sketch the graph of f , then it looks as if the graph of f  may be the same as the cosine curve.
Section 3.3 Derivatives of Trig Functions
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5. Section 3.3 Derivatives of Trig Functions
Example
Prove that the derivative of sin(x) = cos(x).
Section 3.3 Derivatives of Trig Functions
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6. Derivatives of the Trig Functions
Triggy Rules by Matheatre
D’riv-ative of Sine X,
Y’know trig don’t choke.
is Cosine X.
Derivatives of co-functions are-
Derivative of Secant X is, Amazing!
All Negative.
Secant X Tan X!
Ya substitute the functions for the co-functions as implied.
Driv-ative Tangent X:
I said y’know trig don’t choke,
Secant Squared X.
Remember the Chain rule, Chain Rule!
Don’t forget the dx, dx!
Triggy rules, triggy rules,
Triggy, triggy, trigg rules,
Section 3.3 Derivatives of Trig Functions
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7. Derivatives of the Trig Functions
Section 3.3 Derivatives of Trig Functions
Erickson

8. Section 3.3 Derivatives of Trig Functions
Example 1
Find the derivative of the following function:
Section 3.3 Derivatives of Trig Functions
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9. Section 3.3 Derivatives of Trig Functions
Example 2
Find the derivative of the following function:
Section 3.3 Derivatives of Trig Functions
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10. Section 3.3 Derivatives of Trig Functions
Example 3
Find if f (x) = sec x
Section 3.3 Derivatives of Trig Functions
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11. Section 3.3 Derivatives of Trig Functions
Example 4
On a sunny day, a 50-ft flagpole casts a shadow that changes with the elevation of the sun. Let s be the length of the shadow and  the angle of elevation of the sun. Find the rate at which the length of the shadow is changing with respect to  when =45o. Express your answer in units of ft/degree.
Section 3.3 Derivatives of Trig Functions
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12. Section 3.3 Derivatives of Trig Functions
Example 5
As illustrated on the left, suppose a spring with an attached mass is stretched 3 cm beyond its rest position and released at time t = 0. Assuming that the position function of the top of the attached mass is s = -3cost where s is in cm and t is in seconds, find the velocity function and discuss the motion of the attached mass.
Section 3.3 Derivatives of Trig Functions
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13. Section 3.3 Derivatives of Trig Functions
Example 6
Find the equation of the normal and tangent lines to the curve at the given point.
Section 3.3 Derivatives of Trig Functions
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14. Section 3.3 Derivatives of Trig Functions
Example 7
Find the limit
Section 3.3 Derivatives of Trig Functions
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15. Section 3.3 Derivatives of Trig Functions
Example 8
Differentiate.
Section 3.3 Derivatives of Trig Functions
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16. Section 3.3 Derivatives of Trig Functions
Assignment
Page 154 #1-25 odd, odd
Section 3.3 Derivatives of Trig Functions
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