Algebra and Trigonometry,
5th Edition

Preface.
To the Student.
Prologue: Principles of Problem Solving.
P. PREREQUISITES.
Chapter Overview. P1. Modeling the Real-World with Algebra. P2. The Real Numbers. P3. Integer Exponents and Scientific Notation. P4. Rational Exponents and Radicals. P5. Algebraic Expressions. P6. Factoring. P7. Rational Expressions. P8. Solving Basic Equations. P9. Modeling with Equations. Chapter P Review. Chapter P Test.
FOCUS ON MODELING: MAKING THE BEST DECISIONS.
1. EQUATIONS AND GRAPHS.
Chapter Overview. 1.1 The Coordinate Plane. 1.2 Graphs of Equations in Two Variables; Circles. 1.3 Lines. 1.4 Solving Quadratic Equations. 1.5 Complex Numbers. 1.6 Solving Other Types of Equations. 1.7 Solving Inequalities. 1.8 Solving Absolute Value Equations and Inequalities. 1.9 Solving Equations and Inequalities Graphically. 1.10 Modeling Variations. Chapter 1 Review. Chapter 1 Test.
FOCUS ON MODELING: Fitting Lines to Data.
2. FUNCTIONS.
Chapter Overview. 2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models. 2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test.
FOCUS ON MODELING: MODELING WITH FUNCTIONS.
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
Chapter Overview. 3.1. Quadratic Functions and Models. 3.2 Polynomial Functions and Their Graphs. 3.3 Dividing Polynomials. 3.4 Real Zeros of Polynomials. 3.5 Complex Zeros and the Fundamental Theorem of Algebra. 3.6 Rational Functions. 3.7 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test.
FOCUS ON MODELING: FITTING POLYNOMIAL CURVES TO DATA.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Chapter Overview. 4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test.
FOCUS ON MODELING: FITTING EXPONENTIAL AND POWER CURVES TO DATA.
5. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH.
Chapter Overview. 5.1 Angle Measure. 5.2 Trigonometry of Right Triangles. 5.3 Trigonometric Functions of Angles. 5.4 Inverse Trigonometric Functions and Triangles. 5.5 The Law of Sines. 5.6 The Law of Cosines.
Chapter 5 Review. Chapter 5 Test. FOCUS ON MODELING: SURVEYING.
6. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH.
Chapter Overview. 6.1 The Unit Circle. 6.2 Trigonometric Functions of Real Numbers. 6.3 Trigonometric Graphs. 6.4 More Trigonometric Graphs. 6.5 Inverse Trigonometric Functions and Their Graphs. 6.6 Modeling Harmonic Motion. Chapter 6 Review. Chapter 6 Test.
FOCUS ON MODELING: FITTING SINUSOIDAL CURVES TO DATA.
7. CONIC SECTIONS.
Chapter Overview. 7.1 Trigonometric Identities. 7.2 Addition and Subtraction Formulas. 7.3 Double-Angle, Half-Angle, and Sum-Product Formulas. 7.4 Basic Trigonometric Equations. 7.5 More Trigonometric Equations. Chapter 7 Review. Chapter 7 Test.
FOCUS ON MODELING: TRAVELING AND STANDING WAVES.
8. POLAR COORDINATES, PARAMETRIC EQUATIONS, and VECTORS.
Chapter Overview. 8.1 Polar Coordinates. 8.2 Graphs of Polar Equations. 8.3 Polar Form of Complex Numbers; DeMoivre's Theorem. 8.4 Plane Curves and Parametric Equations. 8.5 Vectors in Two Dimensions. 8.6 The Dot Product. Chapter 8 Review. Chapter 8 Test.
FOCUS ON MODELING: THE PATH OF A PROJECTILE.
9. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Chapter Overview. 9.1 Systems of Linear Equations in Two Variables. 9.2 Systems of Linear Equations in Several Variables. 9.3 Partial Fractions. 9.4 Systems of Nonlinear Equations. 9.5 Systems of Inequalities. Chapter 9 Review. Chapter 9 Test.
FOCUS ON MODELING: LINEAR PROGRAMMING.
10. MATRICES AND DETERMINANTS.
Chapter Overview. 10.1 Matrices and Systems of Linear Equations. 10.2 The Algebra of Matrices. 10.3 Inverses of Matrices and Matrix Equations. 10.4 Determinants and Cramer's Rule. Chapter 10 Review. Chapter 10 Test.
FOCUS ON MODELING: COMPUTER GRAPHICS.
11. CONIC SECTIONS.
Chapter Overview. 11.1 Parabolas. 11.2 Ellipses. 11.3 Hyperbolas. 11.4 Shifted Conics. 11.5 Rotation of Axes. 11.6 Polar Equations of Conics. Chapter 11 Review. Chapter 11 Test.
FOCUS ON MODELING: CONICS IN ARCHITECTURE.
12. SEQUENCES AND SERIES.
Chapter Overview. 12.1 Sequences and Summation Notation. 12.2 Arithmetic Sequences. 12.3 Geometric Sequences. 12.4 Mathematical Induction. 12.5 The Binomial Theorem. Chapter 12 Review. Chapter 12 Test.
FOCUS ON MODELING: MODELING WITH RECURSIVE SEQUENCES.
13. COUNTING AND PROBABILITY.
Chapter Overview. 13.1 Counting. 13.2 Probability. 13.3 Binomial Probability. 13.4 Expected Value. Chapter 13 Review. Chapter 13 Test.
FOCUS ON MODELING: THE MONTE CARLO METHOD.
APPENDIX A: Geometry Review.
APPENDIX B: Calculations and Significant Figures.
APPENDIX C: Graphing with a Graphing Calculator.
APPENDIX D: Using the TI-83/84 Graphing Calculator.
Additional Topics
Vectors in Three-Dimensions (available on website)
Mathematics of Finance (available on website)

• James Stewart

  The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He conducted research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Dr. Stewart most recently served as a professor of mathematics at McMaster University, and his research focused on harmonic analysis. Dr. Stewart authored a best-selling calculus textbook series, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS and CALCULUS: CONCEPTS AND CONTEXTS as well as a series of successful precalculus texts.

• Lothar Redlin

  The late Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He was most recently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field was topology.

• Saleem Watson

  Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis. Watson is a co-author on Stewart's best-selling Calculus franchise.

• NEW EXERCISES HELP STUDENTS DEVELOP IMPORTANT PROBLEM-SOLVING SKILLS: New Problem-Solving exercises in most sections highlight and apply a specific problem-solving principle from the prologue. More than 20% of the overall exercises are new to this edition.

• NEW REVIEW MATERIAL REINFORCES STUDENT UNDERSTANDING: Updated, effective review material at the end of most chapters now includes a matching exercise to reinforce the fundamental relationship between graphs and equations. This important review also includes a summary of properties and formulas. In addition, a Concept Check provides a step-by-step review of all the main concepts and applications from the chapter.

• NEW DISCOVERY PROJECTS GUIDE STUDENTS IN APPLYING THE CONCEPTS THEY'VE MASTERED: Several new Discovery Projects in this edition feature applications or extensions of the concepts that students have just studied in the text. Discover/Discuss/Prove/Write problems at the end of every section encourage students to develop and strengthen their conceptual, critical-thinking and writing skills.

• NEW REMEDIAL SUPPORT PREPARES STUDENTS FOR SUCCESS: Revisions throughout Chapter P review prerequisites while WebAssign digital resources provide remedial support to address readiness gaps, including the College Math Readiness Bootcamp and Just-in-Time review exercises. This edition also offers an expanded Geometry Review appendix that now highlights main concepts from geometry used in this edition, including congruence, similarity, the Pythagorean Theorem, parallel lines and circles.

• NEW EXPANDED PROBLEMS IN WEBASSIGN INCLUDE MULTIPLE PARTS TO ENSURE UNDERSTANDING: This edition's new online Expanded Problems take understanding well beyond the basic exercises. These problems ask students to show the specific steps of their work or to explain the reasoning behind the answers they've provided.

• NEW CHAPTER UNITES KEY TOPICS: The new Chapter 8, "Polar Coordinates, Parametric Equations, and Vectors," unites the topics under the theme of describing curves and motion in a coordinate plane. The applications in the chapter demonstrate the need for different coordinate systems. In the "Focus on Modeling" section following the chapter, both parametric equations and vectors are used to model the path and velocity of a projectile.

• WEBASSIGN PROVIDES ONLINE TOOLS TO BUILD YOUR STUDENTS’ CONFIDENCE AND ELEVATE PERFORMANCE: This edition's leading WebAssign digital resources provide instant access to expertly designed support for both you and your students. Updated, innovative exercises, "Explore It" interactive learning modules and instructional videos reinforce concepts for students and assist in review.

• "FOCUS ON MODELING" SECTIONS EMPOWER STUDENTS TO APPLY MATHEMATICS: These "Focus on Modeling" sections illustrate modeling techniques as well as how mathematics can be applied to model real-life situations. These sections teach students how to create their own mathematical models rather than use prefabricated formulas.

• REAL-WORLD APPLICATIONS ENGAGE STUDENTS: This title draws upon applications from engineering, physics, chemistry, business, biology, environmental studies and other fields to demonstrate how mathematics is used to model real-life situations. This approach reinforces the relevance and importance of the principles students are learning.

• TRIGONOMETRY APPROACH PROVIDES FLEXIBILITY IN YOUR INSTRUCTION: The chapters on trigonometry (Chs. 5, 6) are written so you have a choice of beginning with either the right triangle approach or the unit circle approach. Each approach to trigonometry is accompanied by the applications appropriate for that approach. Students clearly understand the reasons behind the different approaches to trigonometry.

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