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1. Graphs and Functions
1.1 The Distance and Midpoint Formulas
1.2 Graphs of Equations; Circles
1.3 Functions and Their Graph
1.4 Properties of Functions
1.5 Library of Functions; Piecewise-defined Functions
1.6 Graphing Techniques: Transformations
1.7 One-to-One Functions; Inverse Functions
2. Trigonometric Functions
2.1 Angles and Their Measure
2.2 Trigonometric Functions: Unit Circle Approach
2.3 Properties of the Trigonometric Functions
2.4 Graphs of the Sine and Cosine Functions
2.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
2.6 Phase Shift; Sinusoidal Curve Fitting
3. Analytic Trigonometry
3.1 The Inverse Sine, Cosine, and Tangent Functions
3.2 The Inverse Trigonometric Functions (continued)
3.3 Trigonometric Equations
3.4 Trigonometric Identities
3.5 Sum and Difference Formulas
3.6 Double-Angle and Half-Angle Formulas
3.7 Product-to-Sum and Sum-to-Product Formulas
4. Applications of Trigonometric Functions
4.1 Right Triangle Trigonometry; Applications
4.2 Law of Sines
4.3 Law of Cosines
4.4 Area of a Triangle
4.5 Simple Harmonic Motion; Damped Motion; Combining Waves
5. Polar Coordinates; Vectors
5.1 Polar Coordinates
5.2 Polar Equations and Graphs
5.3 The Complex Plane; DeMoivre’s Theorem
5.5 The Dot Product
5.6 Vectors in Space
5.7 The Cross Product
6. Analytic Geometry
6.2 The Parabola
6.3 The Ellipse
6.4 The Hyperbola
6.5 Rotation of Axes; General Form of a Conic
6.6 Polar Equations of Conics
6.7 Plane Curves and Parametric Equations
7. Exponential and Logarithmic Functions
7.1 Exponential Functions
7.3 Properties of Logarithms
7.4 Logarithmic and Exponential Equations
7.5 Financial Models
7.6 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
7.7 Building Exponential, Logarithmic, and Logistic Models from Data
Appendix A. Review
A.1 Algebra Essentials
A.2 Geometry Essentials
A.3 Factoring Polynomials; Completing the Square
A.4 Solving Equations
A.5 Complex Numbers; Quadratic Equations in the Complex Number System
A.6 Interval Notation; Solving Inequalities
A.7 nth Roots; Rational Exponents; Radical Equations
A.9 Building Linear Models from Data
Appendix B. Graphing Utilities
B.1 The Viewing Rectangle
B.2 Using a Graphing Utility to Graph Equations
B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
B.4 Using a Graphing Utility to Solve Equations
B.5 Square Screens
B.6 Using a Graphing Utility to Graph a Polar Equation
B.7 Using a Graphing Utility to Graph Parametric
As a professor at an urban public university for over 30 years, I am aware of the varied needs of trigonometry students who range from having little mathematical background and a fear of mathematics courses to those who have had a strong mathematical education and are highly motivated. For some of your students, this will be their last course in mathematics, while others may decide to further their mathematical education. I have written this text for both groups. As the author of precalculus, engineering calculus, finite mathematics, and business calculus texts, and, as a teacher, I understand what students must know if they are to be focused and successful in upper level mathematics courses. However, as a father of four college graduates, I also understand the realities of college life. I have taken great pains to insure that the text contains solid, student-friendly examples and problems, as well as a clear, seamless, writing style. I encourage you to share with me your experiences teaching from this text.
The Sixth Edition builds upon a solid foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. A huge benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions made from colleagues and students who have used previous editions. I am sincerely grateful for thisfeedback and have tried to make changes that improve the flow and usability of the text.
Real Mathematics at Motorola
Each chapter begins with Field Trip to Motorola, a brief description of a current situation at Motorola, followed by Interview at Motorola, a biographical sketch of a Motorola employee. At the end of each chapter is Project at Motorola, written by the Motorola employee, that contains a description, with exercises, of a problem at Motorola that relates to the mathematics found in the chapter. It doesn't get more REAL than this.
Preparing for This Section
Most sections now open with a referenced list (by section and page number) of key items to review in preparation for the section ahead. This provides a just-in-time review for students.
Appendix A Review
This Appendix has been renamed to more accurately reflect its content.
The content here consists of a more detailed version of the first section of the old Chapter 1, an expansion of the material found in the old Appendix A, and Complex Numbers. Although it could be used as the first part of a course in Trigonometry, its real value lies in its use as a just-in-time review of material. Specific references to Appendix A occur throughout the text to assist in the review process. Appropriate use of this appendix will allow students to review when they need to and will allow the instructor more time to cover the course content.
To meet the varied needs of diverse syllabi, this book contains more content than expected in a trigonometry course. The illustration shows the dependencies of chapters on each other.
This book has been organized with flexibility of use in mind. Even within a given chapter, certain sections can be skipped without fear of future problems.
Chapter 1 Functions and Their Graphs
This chapter is now more streamlined than before. A quick coverage of this chapter, which is mainly review material, will enable you to get to Chapter 2 Trigonometric Functions earlier.
Chapter 2 Trigonometric Functions
The sections follow in sequence.
Chapter 3 Analytic Trigonometry
The sections follow in sequence. Sections 3.2, 3.6, and 3.8 may be skipped in a brief course.
Chapter 4 Applications of Trigonometric Functions
The sections follow in sequence. Sections 4.4 and 4.5 may be skipped in a brief course.
Chapter 5 Polar Coordinates; Vectors
Sections 5.1-5.3 and Sections 5.4-5.7 are independent and may be covered separately.
Chapter 6 Analytic Geometry
Sections 6.1-6.4 follow in sequence. Sections 6.5, 6.6, and 6.7 are independent of each other, but do depend on Sections 6.1-6.4.
Chapter 7 Exponential and Logarithmic Functions
Sections 7.1-7.5 follow in sequence; Sections 7.6, 7.7, and 7.8 each require Section 7.3.
As you begin your study of Trigonometry you may feel overwhelmed by the number of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that many elements of Trigonometry are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, just the first in a series of many. Either way, this text was written with you in mind. I have taught trigonometry courses for over thirty years. I am also the father of four college graduates who called home from time to time, frustrated and with questions. I know what you're going through. So I have written a text that doesn't overwhelm, or unnecessarily complicate Trigonometry, while at the same time providing you the skills and practice you need to be successful.
This text is designed to help you, the student, master the terminology and basic concepts of Trigonometry. These aims have helped to shape every aspect of the book. Many learning aids are built into the format of the text to make your study of the material easier and more rewarding. This book is meant to be a "machine for learning," one that can help you focus your efforts and get the most from the time and energy you invest.
First, and most important, this book is meant to be read-so please, begin by reading the material assigned. You will find that the text has additional explanations and examples that will help you. Also, it is best to read the section before the lecture, so you can ask questions right away about anything you didn't understand.
Many sections begin with "Preparing for This Section," a list of concepts that will be used in the section. Take the short amount of time required to refresh your memory. This will make the section easier to understand and will actually save you time and effort.
A list of OBJECTIVES is provided at the beginning of each section. Read them. They will help you recognize the important ideas and skills developed in the section.
After a concept has been introduced and an example given, you will see NOW WORK PROBLEM XX. Go to the exercises at the end of the section, work the problem cited, and check your answer in the back of the book. If you get it right, you can be confident in continuing on in the section. If you don't get it right, go back over the explanations and examples to see what you might have missed. Then rework the problem. Ask for help if you miss it again.
If you follow these practices throughout the section, you will find that you have probably done many of your homework problems. In the exercises, every "Now Work Problem" number is in yellow with a pencil icon . All the odd-numbered problems have answers in the back of the book and worked-out solutions in the Student Solutions Manual supplement. Be sure you have made an honest effort before looking at a worked-out solutes.
At the end of each chapter is a Chapter Review. Use it to be sure you are completely familiar with the equations and formulas listed under "Things to Know." If you are unsure of an item here, use the page reference to go back and review it. Go through the Objectives and be sure you can answer "Yes" to the question "I should be able to ...." If you are uncertain, a page reference to the objective is provided.
Spend the few minutes necessary to answer the "Fill-in-the-Blank" items and the "True/False" items. These are quick and valuable questions to answer.
Lastly, do the problems identified with blue numbers in the Review Exercises. These are my suggestions for a Practice Test. Do some of the other problems in the review for more practice to prepare for your exam.
Please do not hesitate to contact me, through Prentice Hall, with any suggestions or comments that would improve this text. I look forward to hearing from you.