# Algebra and Trigonometry, 3rd Edition Genres:

Book Preface

For many students an Algebra and Trigonometry course represents the first opportunity to discover the beauty and practical power of mathematics. Thus instructors are faced with the challenge of teaching the concepts and skills of the subject while at the same time imparting an appreciation for its effectiveness in modeling the real world. This book aims to help instructors meet this challenge.

In writing this Third Edition, our purpose is to further enhance the usefulness of the book as an instructional tool for teachers and as a learning tool for students. There are several major changes in this edition including a restructuring of each exercise set to better align the exercises with the examples of each section. In this edition each exercise set begins with Concepts Exercises, which encourage students to work with basic concepts and to use mathematical vocabulary appropriately. Several chapters have been reorganized and rewritten (as described below) to further focus the exposition on the main concepts; we have added a new chapter on vectors in two and three dimensions. In all these changes and numerous others (small and large) we have retained the main features that have contributed to the success of this book.

New to the Third Edition

■ Exercises More than 20% of the exercises are new. This includes new Concept Exercises and new Cumulative Review Tests. Key exercises are now linked to examples in the text.
■ Book Companion Website A new website www.stewartmath.com contains Discovery Projects for each chapter and Focus on Problem Solving sections that highlight different problem-solving principles outlined in the Prologue.
■ CHAPTER 3 Functions This chapter has been completely rewritten to focus more sharply on the fundamental and crucial concept of function. The material on quadratic functions, formerly in this chapter, is now part of the chapter on polynomial functions.
■ CHAPTER 4 Polynomial and Rational Functions This chapter now begins with a section on quadratic functions, leading to higher degree polynomial functions.
■ CHAPTER 5 Exponential and Logarithmic Functions The material on the natural exponential function is now in a separate section.
■ CHAPTER 6 Trigonometric Functions: Right Triangle Approach This chapter includes a new section on inverse trigonometric functions and right triangles (Section 6.4) which is needed in applying the Laws of Sines and Cosines in the following section, as well as for solving trigonometric equations in Chapter 8.
■ CHAPTER 7 Trigonometric Functions: Unit Circle Approach This chapter includes a new section on inverse trigonometric functions and their graphs. Introducing this topic here reinforces the function concept in the context of trigonometry.
■ CHAPTER 8 Analytic Trigonometry This chapter has been completely revised. There are two new sections on trigonometric equations (Sections 8.4 and 8.5). The material on this topic (formerly in Section 8.5) has been expanded and revised.
■ CHAPTER 9 Polar Coordinates and Parametric Equations This chapter is now more sharply focused on the concept of a coordinate system. The section on parametric equations is new to this chapter. The material on vectors is now in its own chapter.
■ CHAPTER 10 Vectors in Two and Three Dimensions This is a new chapter with a new Focus on Modeling section.
■ CHAPTER 11 Systems of Equations and Inequalities The material on systems of nonlinear equations is now in a separate section.
■ CHAPTER 12 Conic Sections This chapter is now more closely devoted to the topic of analytic geometry, especially the conic sections; the section on parametric equations has been moved to Chapter 9.