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### Summary

### Summary

This text is designed for a variety of students with different mathematical needs. For those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success in further courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Many of the applied problems in this text are actually real problems that people have had to solve on the job. With an emphasis on problem solving, this text provides students with an excellent opportunity to sharpen their reasoning and thinking skills. With increased critical thinking skills, students will have the confidence they need to tackle whatever future problems they may encounter inside and outside the classroom.

This text is technology optional. With this approach, teachers will be able to offer either a technology-oriented course or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility.

### Author Notes

Mark Dugopolski was born in Menominee, Michigan. After receiving a B.S. from Michigan State University, he taught high school for four years, and then went on to receive an M.S. in mathematics from Northern Illinois University. He also received a Ph.D. in the area of topology from the University of Illinois at Champaign-Urbana, and ever since, Mark has been teaching at Southeastern Louisiana in Hammond, LA. He has been writing textbooks for about fifteen years. He is married and has two daughters, and enjoys playing tennis, jogging, and riding his bicycle in his spare time. Despite the presence of sailboats both on and in his precalculus textbooks, Mark does not sail-- it's his passion for showing students how mathematics is used in the real world that led him to the world of sailing.

### Table of Contents

Preface | p. vii |

Supplements List | p. xi |

Function Gallery | p. xv |

P Algebraic Prerequisites | |

P.1 The Cartesian Coordinate System | p. 2 |

P.2 Functions | p. 12 |

P.3 Families of Functions, Transformations, and Symmetry | p. 20 |

P.4 Compositions and Inverses | p. 31 |

Chapter P Highlights | p. 41 |

Chapter P Review Exercises | p. 42 |

Chapter P Test | p. 44 |

1 Angles and the Trigonometric Functions | |

1.1 Angles and Degree Measure | p. 46 |

1.2 Radian Measure, Arc Length, and Area | p. 55 |

1.3 Angular and Linear Velocity | p. 66 |

1.4 The Trigonometric Functions | p. 72 |

1.5 Right Triangle Trigonometry | p. 83 |

1.6 The Fundamental Identity and Reference Angles | p. 98 |

Chapter 1 Highlights | p. 106 |

Chapter 1 Review Exercises | p. 108 |

Chapter 1 Test | p. 110 |

2 Graphs of the Trigonometric Functions | |

2.1 The Unit Circle and Graphing | p. 112 |

2.2 The General Sine Wave | p. 125 |

2.3 Graphs of the Secant and Cosecant Functions | p. 137 |

2.4 Graphs of the Tangent and Contangent Functions | p. 143 |

2.5 Combining Functions | p. 154 |

Chapter 2 Highlights | p. 161 |

Chapter 2 Review Exercises | p. 162 |

Chapter 2 Test | p. 163 |

Tying it all Together | p. 164 |

3 Trigonometric Identities | |

3.1 Basic Identities | p. 167 |

3.2 Verifying Identities | p. 177 |

3.3 Sum and Difference Identities for Cosine | p. 185 |

3.4 Sum and Difference Identities for Sine and Tangent | p. 192 |

3.5 Double-Angle and Half-Angle Identities | p. 198 |

3.6 Product and Sum Identities | p. 208 |

Chapter 3 Highlights | p. 218 |

Chapter 3 Review Exercises | p. 219 |

Chapter 3 Test | p. 221 |

Tying it all Together | p. 222 |

4 Solving Conditional Trigonometric Equations | |

4.1 The Inverse Trigonometric Functions | p. 224 |

4.2 Basic Sine, Cosine, and Tangent Equations | p. 235 |

4.3 Multiple Angle Equations | p. 249 |

4.4 Trigonometric Equations of Quadratic Type | p. 255 |

Chapter 4 Highlights | p. 262 |

Chapter 4 Review Exercises | p. 263 |

Chapter 4 Test | p. 265 |

Tying it all Together | p. 266 |

5 Applications of Trigonometry | |

5.1 The Law of Sines | p. 268 |

5.2 The Law of Cosines | p. 280 |

5.3 Area of a Triangle | p. 291 |

5.4 Vectors | p. 298 |

5.5 Applications of Vectors | p. 310 |

Chapter 5 Highlights | p. 320 |

Chapter 5 Review Exercises | p. 321 |

Chapter 5 Test | p. 323 |

Tying it all Together | p. 323 |

6 Complex Numbers, Polar Coordinates, and Parametric Equations | |

6.1 Complex Numbers | p. 325 |

6.2 Trigonometric Form of Complex Numbers | p. 333 |

6.3 Powers and Roots of Complex Numbers | p. 341 |

6.4 Polar Equations | p. 347 |

6.5 Parametric Equations | p. 358 |

Chapter 6 Highlights | p. 363 |

Chapter 6 Review Exercises | p. 364 |

Chapter 6 Test | p. 366 |

Tying it all Together | p. 366 |

Appendix A Solutions to Try This Exercises | p. S-1 |

Appendix B More Thinking Outside the Box | p. S-15 |

Answers to Selected Exercises | p. A-1 |

Credits | p. C-1 |

Index of Applications | p. I-1 |

Index | p. I-3 |