Chapter 3 Derivatives Section 3 5 Derivatives of

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Chapter 3 Derivatives Section 3. 5 Derivatives of Trigonometric Functions Copyright © 2015, 2012,

Chapter 3 Derivatives Section 3. 5 Derivatives of Trigonometric Functions Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 2

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 2

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3

Quick Review Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 3

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 4

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5

Quick Review Solutions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 5

What you’ll learn about n n n Derivatives of the sine and cosine functions

What you’ll learn about n n n Derivatives of the sine and cosine functions Modeling harmonic motion Jerk as the derivative of acceleration Derivatives of the tangent, cotangent, secant, and cosecant functions Tangent and normal lines … and why The derivatives of sines and cosines play a key role in describing periodic change. Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 6

Derivative of the Sine Function Copyright © 2016, 2012, and 2010 Pearson Education, Inc.

Derivative of the Sine Function Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 7

Derivative of the Cosine Function Copyright © 2016, 2012, and 2010 Pearson Education, Inc.

Derivative of the Cosine Function Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 8

Example Finding the Derivative of the Sine and Cosine Functions Copyright © 2016, 2012,

Example Finding the Derivative of the Sine and Cosine Functions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 9

Simple Harmonic Motion The motion of a weight bobbing up and down on the

Simple Harmonic Motion The motion of a weight bobbing up and down on the end of a string is an example of simple harmonic motion. Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 10

Example Simple Harmonic Motion Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 11

Example Simple Harmonic Motion Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 11

Jerk Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 12

Jerk Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 12

Derivative of the Other Basic Trigonometric Functions Copyright © 2016, 2012, and 2010 Pearson

Derivative of the Other Basic Trigonometric Functions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 13

Example Derivative of the Other Basic Trigonometric Functions Copyright © 2016, 2012, and 2010

Example Derivative of the Other Basic Trigonometric Functions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 14

Example Derivative of the Other Basic Trigonometric Functions Copyright © 2016, 2012, and 2010

Example Derivative of the Other Basic Trigonometric Functions Copyright © 2016, 2012, and 2010 Pearson Education, Inc. 15

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