Limits and Derivatives

Chapter 3 Differentiation Rules3.3 Derivatives of Trig Functions1Section 3.3 Derivatives of Trig FunctionsEricksonSection 3.3 Derivatives of Trig Functions2Remember

*This functions represents the inverse sin of x (arcsinx) and not any of the other listed functions.EricksonDefinitions

3Section 3.3 Derivatives of Trig FunctionsEricksonIf 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 Functions4Derivative: Sine

EricksonProve that the derivative of sin(x) = cos(x).Example

5Section 3.3 Derivatives of Trig FunctionsEricksonTriggy Rules by Matheatre

Driv-ative of Sine X, is Cosine X.Derivative of Secant X is, Amazing! Secant X Tan X!Driv-ative Tangent X: Secant Squared X.Remember the Chain rule, Chain Rule! Dont forget the dx, dx!Triggy rules, triggy rules, Triggy, triggy, trigg rules,Triggy rules, triggy rules, Triggy, triggy, trigg rules,

Yknow trig dont choke. Derivatives of co-functions are- All Negative.Ya substitute the functions for the co-functions as implied.I said yknow trig dont choke, Derivatives of co-functions are- All Negative.Ya substitute the functions for the co-functions as implied.

Section 3.3 Derivatives of Trig Functions6Derivatives of the Trig Functions

EricksonDerivatives of the Trig Functions

7Section 3.3 Derivatives of Trig FunctionsEricksonFind the derivative of the following function:Example 1

8Section 3.3 Derivatives of Trig FunctionsEricksonFind the derivative of the following function:Example 2

9Section 3.3 Derivatives of Trig FunctionsEricksonFind if f (x) = sec x Example 3

10Section 3.3 Derivatives of Trig FunctionsEricksonOn 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.Example 4

11Section 3.3 Derivatives of Trig FunctionsErickson

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.Example 512Section 3.3 Derivatives of Trig FunctionsEricksonFind the equation of the normal and tangent lines to the curve at the given point.Example 613Section 3.3 Derivatives of Trig Functions

Erickson13Find the limitSection 3.3 Derivatives of Trig Functions14Example 7

EricksonDifferentiate.Section 3.3 Derivatives of Trig Functions15Example 8

EricksonPage 154 #1-25 odd, 39-49 oddAssignment16Section 3.3 Derivatives of Trig FunctionsEricksonTriggy RulesMatheatreCalculus: The Musical! 2nd Edition., track 04/08experimental63215.027