Trigonometry (10th Edition) by Margaret L. Lial

Book Preface

As authors, we have called upon our classroom experiences, use of MyMathLab, suggestions from users and reviewers, and many years of writing to provide tools that will support learning and teaching. This new edition of Trigonometry continues our effort to provide a sound pedagogical approach through logical development of the subject matter. This approach forms the basis for all of the Lial team’s instructional materials available from Pearson Education, in both print and technology forms.

Our goal is to produce a textbook that will be an integral component of the, student’s experience in learning trigonometry. With this in mind, we have provided a textbook that students can read more easily, which is often a difficult task, given the nature of mathematical language. We have also improved page layouts for better flow, provided additional side comments, and updated many figures.

We realize that today’s classroom experience is evolving and that technologybased teaching and learning aids have become essential to address the ever-changing needs of instructors and students. As a result, we’ve worked to provide support for all classroom types—traditional, hybrid, and online. In the 10th edition, text and online materials are more tightly integrated than ever before. This enhances flexibility and ease of use for instructors and increases success for students. See pages xvii–xix for descriptions of these materials.

New to the 10th Edition

– In Chapter 1 we begin our effort in using more side comments in Examples and providing better pairing of even and odd exercises in our exercise sets. InSection 1.4, we have provided a better visual in the figure (Figure 34) accompanying the explanation of the ranges of the sine  and cosine functions (ratios) in conjunction with right triangles.
– In Chapter 2 we have added new exercises for evaluating trigonometric expressions with function values of special angles (Section 2.2, Exercises 45–52).

We have updated the discussion on using inverse trigonometric functions to find angle measures using a calculator (Section 2.3 throughout), and we have updated examples of solving right triangles to prepare students for the more challenging exercises in the Exercise sets (Sections 2.4 and 2.5).
– In Chapter 3 we have added a figure (Figure 2) clarifying the concept of radian measure. In Section 3.2 there are new exercises involving application of the formula for the area of a circle (Exercises 61–64). Section 3.3 now includes an expanded explanation of what values a calculator returns for inverse trigonometric functions. We have added a new figure in Example 4 explaining how to use the concept of inverse functions. There is a new subhead “Expressing Function Values as Lengths of Line Segments” along with a newexample (Example 6) and exercises (Exercises 87 and 88).
– In Chapter 4 we have an updated figure and discussion relating the sine function to the unit circle (Section 4.1, Figure 4, and discussion). We have expanded the discussion of sketching graphs of translated trigonometric functions and have updated the guidelines for these sketches (Section 4.2). We have included new examples of connecting graphs with equations (Section 4.1, Example 6 and Section 4.3, Example 6), and have included new exercises of this type in the exercise sets and chapter review exercises.
– In Chapter 5 we have rewritten the solution of Example 4 in Section 5.3 to illustrate how this standard type of problem can be solved by either using the Pythagorean identities or using angles in standard position. In Exercises 73–84 of Section 5.6, we now discuss the rarely-studied exact function values of 18° and 72° angles.
– In Chapter 6 we have updated the discussion on finding inverse function values using a calculator (Section 6.1). We have included updated examples and many more exercises in which trigonometric equations are solved for all solutions in both degrees and radians. Several new figures are included relating solutions of trigonometric equations with angle measures and arc lengths on the unit circle (Sections 6.2 and 6.3). For equations involving inverse trigonometric functions that are solved for a specified variable, restrictions are now given so that each equation provides a one-to-one correspondence, and a new figure is given to provide conceptual understanding (Section 6.4).
– In Chapter 7 we have updated and improved many of the illustrations in the examples and exercises. In Section 7.4 the new Figures 35 and 37 illustrate operations with vectors geometrically, and we have also included the justification for the geometric interpretation of the dot product. Section 7.5 now includes a new example (Example 5) illustrating vectors applied to a navigation problem. This type of problem is always troublesome for students.
– In Chapter 8 we have rewritten the introduction to the set of complex numbers and have included a new diagram illustrating the relationships among its subsets. Polar graphs now include underlying grids for easier placement of polar coordinates.
– For visual learners, numbered Figure and Example references within the text are set using the same typeface as the figure and bold print for the example.
This makes it easier for the students to identify and connect them. We also have increased our use of a “drop down” style, when appropriate, to distinguish between simplifying expressions and solving equations, and we have added many more explanatory side comments. Interactive figures with accompanying exercises and explorations are now available and assignable in MyMathLab.
– Enhancing the already well-respected exercises, hundreds are new or modified, and many present updated real-life data. In addition, the MyMathLab course has expanded coverage of all exercise types appearing in the exercise sets, as well as the mid-chapter Quizzes and Summary Exercises.

Features of this Text
SUPPORT FOR LEARNING CONCEPTS

We provide a variety of features to support students’ learning of the essential topics of trigonometry. Explanations that are written in understandable terms, figures and graphs that illustrate examples and concepts, graphing technology that supports and enhances algebraic manipulations, and real-life applications that enrich the topics with meaning all provide opportunities for students to deepen their understanding of mathematics. These features help students make mathematical connections and expand their own knowledge base.
– Examples Numbered examples that illustrate the techniques for working exercises are found in every section. We use traditional explanations, side comments, and pointers to describe the steps taken—and to warn students about common pitfalls. Some examples provide additional graphing calculator solutions, although these can be omitted if desired.

– Now Try Exercises Following each numbered example, the student is directed to try a corresponding odd-numbered exercise (or exercises).
This feature allows for quick feedback to determine whether the student has understood the principles illustrated in the example.
– Real-Life Applications We have included hundreds of real-life applications, many with data updated from the previous edition. They come from fields such as astronomy, meteorology, environmental studies, construction, biology and life sciences, music, and physics.
– Function Boxes Beginning in Chapter 4, special function boxes (for example, see page 135) offer a comprehensive, visual introduction to each type of function and also serve as an excellent resource for reference and review. Each function box includes a table of values, traditional and calculatorgenerated graphs, the domain, the range, and other special information about the function. These boxes are now assignable in MyMathLab.
– Figures and Photos Today’s students are more visually oriented than ever before, and we have updated the figures in this edition to a greater extent than in our previous few editions. Interactive figures with accompanying exercises and explorations are now available and assignable in MyMathLab.
– Use of Graphing Technology We have integrated the use of graphing calculators where appropriate, although this technology is completely optional and can be omitted without loss of continuity. We continue to stress that graphing calculators support understanding but that students must first master the underlying mathematical concepts. Exercises that require their use are marked with an icon .
– Cautions and Notes Text that is marked Caution warns students of common errors, and NOTE comments point out explanations that should receive particular attention.
– Looking Ahead to Calculus These margin notes offer glimpses of how the topics currently being studied are used in calculus.