Trigonometry, 12th Edition © 2021

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.

When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh), and has been an avid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

A native Midwesterner, Terry McGinnis received her Bachelor’s of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in both developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.

Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks where she earned a bachelor’s degree in Secondary Mathematics Education. She has two master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri–Rolla, the second in Adult Education from the University of Missouri–St. Louis. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding. She is able to pursue these interests as a contributor on the Lial Developmental Math series, and a co-author on the Precalculus series.

Preface

Resources for Success

R. Algebra Review
R.1 Basic Concepts from Algebra
R.2 Real Number Operations and Properties
R.3 Exponents, Polynomials, and Factoring
R.4 Rational Expressions
R.5 Radical Expressions
R.6 Equations and Inequalities
R. 7 Rectangular Coordinates and Graphs
R.8 Functions
R.9 Graphing Techniques

1. Trigonometric Functions
1-1 Angles
1-2 Angle Relationships and Similar Triangles
1-3 Trigonometric Functions
1-4 Using the Definitions of the Trigonometric Functions
Test Prep
Review Exercises
Test

2. Acute Angles and Right Triangles
2-1 Trigonometric Functions of Acute Angles
2-2 Trigonometric Functions of Non-Acute Angles
2-3 Approximations of Trigonometric Function Values
2-4 Solutions and Applications of Right Triangles
2-5 Further Applications of Right Triangles
Test Prep
Review Exercises
Test

3. Radian Measure and the Unit Circle
3-1 Radian Measure
3-2 Applications of Radian Measure
3-3 The Unit Circle and Circular Functions
3-4 Linear and Angular Speed
Test Prep
Review Exercises
Test

4. Graphs of the Circular Functions
4-1 Graphs of the Sine and Cosine Functions
4-2 Translations of the Graphs of Sine and Cosine Functions
4-3 Graphs of the Tangent and Cotangent Functions
4-4 Graphs of the Secant and Cosecant Functions
4-5 Harmonic Motion
Test Prep
Review Exercises
Test

5. Trigonometric Identities
5-1 Fundamental Identities
5-2 Verifying Trigonometric Identities
5-3 Sum and Difference Identities for Cosine
5-4 Sum and Difference Identities for Sine and Tangent
5-5 Double-Angle Identities
5-6 Half-Angle Identities
Test Prep
Review Exercises
Test

6. Inverse Circular Functions and Trigonometric Equations
6-1 Inverse Circular Functions
6-2 Trigonometric Equations I
6-3 Trigonometric Equations II
6-4 Equations Involving Inverse Trigonometric Functions
Test Prep
Review Exercises
Test

7. Applications of Trigonometry and Vectors
7-1 Oblique Triangles and the Law of Sines
7-2 The Ambiguous Case of the Law of Sines
7-3 The Law of Cosines
7-4 Geometrically Defined Vectors and Applications
7-5 Algebraically Defined Vectors and the Dot Product
Test Prep
Review Exercises
Test

8. Complex Numbers, Polar Equations, and Parametric Equations
8-1 Complex Numbers
8-2 Trigonometric (Polar) Form of Complex Numbers
8-3 The Product and Quotient Theorems
8-4 De Moivre’s Theorem
8-5 Polar Equations and Graphs
8-6 Parametric Equations, Graphs, and Applications
Test Prep
Review Exercises
Test

Answers to Selected Exercises
Photo Credits
Index