9780134433042

For courses in Precalculus.

Providing the rigor of solid mathematics with an engaging and friendly 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.

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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

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Precalculus A Unit Circle Approach

Precalculus A Unit Circle Approach

0134433041

Summary

Table of Contents

Supplemental Materials