Precalculus (3^rd Ed.) A Unit Circle Approach

As teachers, Ratti and McWaters saw firsthand where their Precalculus and Calculus students struggled, where they needed help making connections, and what material they needed to be successful in calculus. They decided to partner and write this text with the primary goal of preparing students to be successful in calculus and future STEM courses. Their experience in the classroom shows in each chapter. The focus on conceptual development, real-life applications, and extensive exercises, encourages a deeper understanding of the mathematics. Precalculus: A Unit Circle Approach, 3rd Edition, includes thorough coverage of topics as preparation for calculus, including; trig identities, difference quotient, functional composition, decomposition and emphasizes graphing techniques/transformations.

1. Graphs and Functions

1.1 Graphs of Equations

1.2 Lines

1.3 Functions

1.4 A Library of Functions

1.5 Transformations of Functions

1.6 Combining Functions; Composite Functions

1.7 Inverse Functions

2. Polynomial and Rational Functions

2.1 Quadratic Functions

2.2 Polynomial Functions

2.3 Dividing Polynomials and the Rational Zeros Test

2.4 Rational Functions

2.5 Polynomial and Rational Inequalities

2.6 Zeros of a Polynomial Function

2.7 Variation

3. Exponential and Logarithmic Functions

3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Rules of Logarithms

3.4 Exponential and Logarithmic Equations and Inequalities

3.5 Logarithmic Scales; Modeling

4. Trigonometric Functions

4.1 Angles and Their Measure

4.2 The Unit Circle; Trigonometric Functions of Real Numbers

4.3 Trigonometric Functions of Angles

4.4 Graphs of the Sine and Cosine Functions

4.5 Graphs of the Other Trigonometric Functions

4.6 Inverse Trigonometric Functions

5. Analytic Trigonometry

5.1 Trigonometric Identities

5.2 Sum and Difference Formulas

5.3 Double-Angle and Half-Angle Formulas

5.4 Product-to-Sum and Sum-to-Product Formulas

5.5 Trigonometric Equations

6. Applications of Trigonometric Functions

6.1 Right-Triangle Trigonometry

6.2 The Law of Sines

6.3 The Law of Cosines

6.4 Vectors

6.5 The Dot Product

6.6 Polar Coordinates

6.7 Polar Form of Complex Numbers; DeMoivre’s Theorem

7. Systems of Equations and Inequalities

7.1 Systems of Equations in Two Variables

7.2 Systems of Linear Equations in Three Variables

7.3 Systems of Inequalities

7.4 Matrices and Systems of Equations

7.5 Determinants and Cramer’s Rule

7.6 Partial-Fraction Decomposition

7.7 Matrix Algebra

7.8 The Matrix Inverse

8.  Analytic Geometry

8.1 Conic Sections: Overview

8.2 The Parabola

8.3 The Ellipse

8.4 The Hyperbola

8.5 Rotation of Axes

8.6 Polar Equations of Conics

8.7 Parametric Equations

9. Further Topics in Algebra

9.1 Sequences and Series

9.2 Arithmetic Sequences; Partial Sums

9.3 Geometric Sequences and Series

9.4 Mathematical Induction

9.5 The Binomial Theorem

9.6 Counting Principles

9.7 Probability

10. An Introduction to Calculus

10.1 Finding Limits Using Tables and Graphs

10.2 Finding Limits Algebraically

10.3 Infinite Limits and Limits at Infinity

10.4 Introduction to Derivatives

10.5 Area and the Integral

Appendix A. Review

A.1 The Real Numbers; Integer Exponents

A.2 Polynomials

A.3 Rational Expressions

A.4 Radical and Rational Exponents

A.5 Topics in Geometry

A.6 Equations

A.7 Inequalities

A.8 Complex Numbers

Precalculus: A Unit Circle Approach offers rigorous topics ideal for students heading for calculus, in a friendly, “teacherly” tone.

• Functions are presented in Chapter 1, building a foundation for a strong preparation for calculus.
• Trigonometric functions are introduced in Chapter 4 with a unit circle approach, before developing the right triangle.
• Right triangle applications (height and distance) are covered in Chapter 6, Applications of Trigonometric Functions.

• Student-friendly support features in Ratti/McWaters are designed to help students to see not only what they are going to learn, but also why, so that every concept is given the proper context.
  • NEW! Additional Review Material.  We have provided additional review material in Chapters 1 and 2 that users of the previous editions identified as material they had to supplement or as requiring reference to the appendix.
  • Topics for review help students refresh their memories on essential topics before beginning each chapter, listing specific page references to make it easy to find those concepts.
  • Clear Objectives preview the key points of the section ahead, providing easy reference points when studying for exams. These Objectives appear again at the appropriate places in the section, putting each new topic into context.
  • Every section opens with an engaging Application that is revisited later in the section through examples and exercises. The Application ties key ideas together and provides motivation for students to read and study.
• Work it out: As you would in your own class, Ratti and McWaters encourage students to practice the material f