Trigonometry, 12th edition

Margaret L. Lial American River College
John Hornsby University of New Orleans
David I. Schneider University of Maryland
Callie J. Daniels St. Charles Community College

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Trigonometry channels the experience of master teachers to help students develop the conceptual understanding and analytical skills needed to succeed in mathematics. A systematic approach is used to present each topic and is designed to actively engage students in learning. Ample opportunities for review are interspersed within chapters and also found at the end of chapters. The 12th Edition offers a complete suite of materials that supports all classroom types and learners.

Hallmark features of this title

The variety of exercise types promotes understanding and reduces rote memorization.
Concept Preview exercises begin each homework section to ensure students' understanding of vocabulary and basic concepts, especially for hybrid, online and flipped courses.
Concept Check exercises focus on mathematical thinking and conceptual understanding.
Relating Concepts exercises help students connect topics and develop problem-solving skills as they compare ideas, identify and describe patterns, and extend concepts to new situations.
Pointers in the examples provide on-the-spot reminders and warnings about common pitfalls.
Now Try exercises conclude every example with a reference to one or more parallel, odd-numbered exercises from the corresponding exercise set.

New and updated features of this title

Expanded Chapter R includes more basic concepts that often challenge students, including a new section on Fractions, Decimals, and Percents. Additional new topics throughout the chapter include operations with signed numbers, dividing a polynomial by a monomial, and factoring expressions with negative and rational exponents. Topics are reorganized for improved flow throughout the chapter.
Careful addition of exercises in Chapters 1 and 2 covers the topics of Functions (Section 2.3), Graphs of Basic Functions (Section 2.6), Linear Functions (Section 2.4), Function Operations and Composition (2.8), and more.
A new section on Polynomial and Rational Inequalities in Chapter 3 features a visual approach to solving such inequalities by interpreting the graphs of related functions.
Updated exercises and examples:
- New exercises in Section 4.3 (Logarithmic Functions) relate exponential and logarithmic functions as inverses. A new example and related exercises in Section 5.2 (Matrix Solution of Linear Systems) use Gaussian elimination to solve linear systems of equations.
- A new example and related exercises in Sections 6.2 (Ellipses) and 6.3 (Hyperbolas) have been added, in which completing the square is used to find the standard form of an ellipse or a hyperbola.

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

About our authors

The late Marge Lial 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 25 years of teaching at the high school and university levels and 15 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.

David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT. He is currently an emeritus professor of mathematics at the University of Maryland. He has authored 8 widely used math texts, 14 highly acclaimed computer books, and 3 widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.

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.

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