**Pre-Calculus with Trigonometry (Second Edition)**

**General Information**

Table of Contents

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**Chapter 1: Packing Your Suitcase: Tools for Your Journey**

**Chapter 2: Finding the Area Under a Curve**

**Chapter 3: Exponentials and Logarithms**

**Chapter 4: Circular Functions**

**Chapter 5: Introduction to Limits**

**Chapter 6: Extending Periodic Functions**

**Chapter 7: Algebra for College Mathematics: Problem Solving 101**

**Chapter 8: More on Limits**

**Chapter 9: Rates of Change**

**Chapter 10: Vectors and Parametric Equations**

**Chapter 11: Polar Equations and Complex Numbers**

**Chapter 12: Linear Transformations: Applications of Matrices**

**Chapter 13: Conic Sections: Readiness for College Math Text**

**Glossary**

**Index**

Opening | 1.OP | Chapter Opening |

Section 1.1 | 1.1.1 | Finding Functions Using View Tubes |

1.1.2 | Transformations of Parent Graphs | |

1.1.3 | Basic Inverses and Function Operations | |

1.1.4 | Transformations of Arbitrary Graphs | |

Section 1.2 | 1.2.1 | Programming Introduction and Point-Slope Form of a Line |

1.2.2 | Programming Formulas and Experiments | |

Section 1.3 | 1.3.1 | Solving Non-Right Triangles |

1.3.2 | Solving Non-Right Triangles, Continued | |

Section 1.4 | 1.4.1 | Radian as a Unit of Measure |

1.4.2 | Radians in the Unit Circle | |

Closure | 1.CL | Chapter Closure |

Opening | 2.OP | Chapter Opening |

Section 2.1 | 2.1.1 | Piecewise Functions and an Intuitive Idea of Continuity |

2.1.2 | Shifting Functions and Periodicity | |

Section 2.2 | 2.2.1 | Summation and Sigma Notation |

2.2.2 | Programming a Sum | |

Section 2.3 | 2.3.1 | Area Under a Curve: Part I |

2.3.2 | Area Under a Curve: Part II | |

2.3.3 | Area Under a Curve: Part III | |

2.3.4 | Shifting Area | |

2.3.5 | Trapping Area with Trapezoids | |

2.3.6 | Going All to Pieces: Writing an Area Program | |

2.3.7 | Area as a Function | |

2.3.8 | Rocket Launch | |

Closure | 2.CL | Chapter Closure |

Opening | 3.OP | Chapter Opening |

Section 3.1 | 3.1.1 | Horizontal and Vertical Stretches |

3.1.2 | Applications of Exponential Functions | |

3.1.3 | Stretching Exponential Functions | |

Section 3.2 | 3.2.1 | Inverses |

3.2.2 | Logs as Inverse Exponentials | |

3.2.3 | Graphing Log Functions | |

Section 3.3 | 3.3.1 | Working Within the Law |

3.3.2 | Solving Exponential Functions and Finding Logs with Bases Other Than Ten | |

Closure | 3.CL | Chapter Closure |

Opening | 4.OP | Chapter Opening |

Section 4.1 | 4.1.1 | Special Angles in the Unit Circle |

4.1.2 | Sine and Cosine in the Unit Circle | |

4.1.3 | Graphs of Sine and Cosine | |

4.1.4 | Shifts of Sine and Cosine | |

Section 4.2 | 4.2.1 | Reciprocal Trig Functions and Pythagorean Identities |

4.2.2 | Simplifying Trig Expressions | |

4.2.3 | Frequency of Sine and Cosine Graphs | |

4.2.4 | Working With Trig Identities | |

Section 4.3 | 4.3.1 | Applications of Trig Functions |

4.3.2 | Sine Here and Have Your Parents Cosine | |

Closure | 4.CL | Chapter Closure |

Opening | 5.OP | Chapter Opening |

Section 5.1 | 5.1.1 | View Tube With a Twist |

5.1.2 | Simplifying Rational Functions and Identifying Them as Shifts | |

5.1.3 | Graphing Reciprocals of Functions | |

Section 5.2 | 5.2.1 | Introduction to Limits |

5.2.2 | A Different Approach to Limits | |

5.2.3 | Working With One-Sided Limits | |

5.2.4 | More on Limits | |

5.2.5 | Piecewise Functions and Limits | |

Closure | 5.CL | Chapter Closure |

Opening | 6.OP | Chapter Opening |

Section 6.1 | 6.1.1 | Solving Trig Equations |

6.1.2 | Inverse Sine and Cosine: Solutions my Calculator Never Told Me | |

6.1.3 | The Ambiguous Case of the Law of Sines | |

6.1.4 | Graphs of Tangent and Inverse Tangent | |

Section 6.2 | 6.2.1 | Putting all of the Transformations Together |

6.2.2 | Angle Sum and Difference Formulas | |

6.2.3 | Modeling With Periodic Functions | |

Section 6.3 | 6.3.1 | Double-Angle Formulas |

6.3.2 | Solving More Complex Trig Equations | |

Section 6.4 | 6.4.1 | The Spring Problem |

6.4.2 | Improving the Spring Problem | |

Closure | 6.CL | Chapter Closure |

Opening | 7.OP | Chapter Opening |

Section 7.1 | 7.1.1 | Describing Functions |

7.1.2 | Describing Functions, Continued | |

Section 7.2 | 7.2.1 | Setting up Word Problems |

7.2.2 | Make Your Life Easier by Decomposing Functions | |

7.2.3 | Polynomial Division | |

7.2.4 | Binomial Expansion From Pascal’s Triangle | |

Section 7.3 | 7.3.1 | Easy Ways to Add Special Series |

7.3.2 | Geometric Series | |

7.3.3 | Binomial Probabilities | |

Closure | 7.CL | Chapter Closure |

Opening | 8.OP | Chapter Opening |

Section 8.1 | 8.1.1 | A Race to Infinity |

8.1.2 | Limit of Rational Functions | |

8.1.3 | Surprising Rational Functions | |

8.1.4 | Putting the Squeeze on π | |

Section 8.2 | 8.2.1 | The Number e |

8.2.2 | Applications of e | |

8.2.3 | Infinite Geometric Series | |

8.2.4 | The Sum of the Harmonic Series | |

8.2.5 | The Fibonacci Sequence | |

8.2.6 | Proof by Induction | |

Closure | 8.CL | Chapter Closure |

Opening | 9.OP | Chapter Opening |

Section 9.1 | 9.1.1 | Rates of Change From Data |

9.1.2 | More Rates of Change From Data | |

9.1.3 | Slopes and Rates of Change | |

9.1.4 | Average Velocity and Rates of Change | |

Section 9.2 | 9.2.1 | Moving From AROC to IROC |

9.2.2 | Secant and Tangent Lines | |

Closure | 9.CL | Chapter Closure |

Opening | 10.OP | Chapter Opening |

Section 10.1 | 10.1.1 | An Introduction to Vectors |

10.1.2 | Working with Vectors | |

10.1.3 | Applications of Vectors | |

10.1.4 | The Dot Product | |

Section 10.2 | 10.2.1 | Introduction to Parametric Equations |

10.2.2 | Graphing Parametric Equations Using a Calculator | |

10.2.3 | Applications of Parametric Equations | |

Closure | 10.CL | Chapter Closure |

Opening | 11.OP | Chapter Opening |

Section 11.1 | 11.1.1 | Plotting Polar Coordinates by Hand |

11.1.2 | Graphs of Polar Equations | |

11.1.3 | Rotating Polar Curves | |

11.1.4 | A Polar Exploration | |

Section 11.2 | 11.2.1 | Using the Complex Plane |

11.2.2 | Powers and Roots of Complex Numbers | |

Closure | 11.CL | Chapter Closure |

Opening | 12.OP | Chapter Opening |

Section 12.1 | 12.1.1 | Basic Operations Using Matrices |

12.1.2 | Using Matrix Equations to Solve Systems | |

12.1.3 | Applications of Matrices | |

Section 12.2 | 12.2.1 | Using Matrices to Complete Linear Transformations |

12.2.2 | Composition of Transformations | |

12.2.3 | Properties of Transformations | |

Closure | 12.CL | Chapter Closure |

Opening | 13.OP | Chapter Opening |

Section 13.1 | 13.1.1 | Circles |

13.1.2 | Ellipses | |

13.1.3 | Hyperbolas | |

13.1.4 | Parabolas | |

Section 13.2 | 13.2.1 | Second-Degree Equations |

Closure | 13.CL | Chapter Closure |