College Algebra and Trigonometry

<h2>Table of Contents</h2> <p> </p> <ol> <li><strong>BASIC CONCEPTS OF ALGEBRA</strong> <ul> <li>P.1 The Real Numbers and Their Properties</li> <li>P.2 Integer Exponents and Scientific Notation</li> <li>P.3 Polynomials</li> <li>P.4 Factoring Polynomials</li> <li>P.5 Rational Expressions</li> <li>P.6 Rational Exponents and Radicals</li> <li>Chapter P Review and Tests</li> <li>Review Exercises</li> <li>Practice Test</li> </ul></li> <li><strong>EQUATIONS AND INEQUALITIES</strong> <ul> <li>1.1 Linear Equations in One Variable</li> <li>1.2 Applications of Linear Equations: Modeling</li> <li>1.3 Quadratic Equations</li> <li>1.4 Complex Numbers: Quadratic Equations with Complex Solutions</li> <li>1.5 Solving Other Types of Equations</li> <li>1.6 Inequalities</li> <li>1.7 Equations and Inequalities Involving Absolute Value</li> <li>Chapter 1 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> </ul></li> <li><strong>GRAPHS AND FUNCTIONS</strong> <ul> <li>2.1 The Coordinate Plane</li> <li>2.2 Graphs of Equations</li> <li>2.3 Lines</li> <li>2.4 Functions</li> <li>2.5 Properties of Functions</li> <li>2.6 A Library of Functions</li> <li>2.7 Transformations of Functions</li> <li>2.8 Combining Functions; Composite Functions</li> <li>2.9 Inverse Functions</li> <li>Chapter 2 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—2</li> </ul></li> <li><strong>POLYNOMIAL AND RATIONAL FUNCTIONS</strong> <ul> <li>3.1 Quadratic Functions</li> <li>3.2 Polynomial Functions</li> <li>3.3 Dividing Polynomials</li> <li>3.4 The Real Zeros of a Polynomial Function</li> <li>3.5 The Complex Zeros of a Polynomial Function</li> <li>3.6 Rational Functions</li> <li>3.7 Variation</li> <li>Chapter 3 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—3</li> </ul></li> <li><strong>EXPONENTIAL AND LOGARITHMIC FUNCTIONS</strong> <ul> <li>4.1 Exponential Functions</li> <li>4.2 Logarithmic Functions</li> <li>4.3 Rules of Logarithms</li> <li>4.4 Exponential and Logarithmic Equations and Inequalities</li> <li>4.5 Logarithmic Scales; Modeling</li> <li>Chapter 4 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—4</li> </ul></li> <li><strong>TRIGONOMETRIC FUNCTIONS</strong> <ul> <li>5.1 Angles and Their Measure</li> <li>5.2 Right-Triangle Trigonometry</li> <li>5.3 Trigonometric Functions of Any Angle; The Unit Circle</li> <li>5.4 Graphs of the Sine and Cosine Functions</li> <li>5.5 Graphs of the Other Trigonometric Functions</li> <li>5.6 Inverse Trigonometric Functions</li> <li>Chapter 5 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—5</li> </ul></li> <li><strong>TRIGONOMETRIC IDENTITIES AND EQUATIONS</strong> <ul> <li>6.1 Trigonometric Identities</li> <li>6.2 Sum and Difference Formulas</li> <li>6.3 Double-Angle and Half-Angle Formulas</li> <li>6.4 Product-to-Sum and Sum-to-Product Formulas</li> <li>6.5 Trigonometric Equations I</li> <li>6.6 Trigonometric Equations II</li> <li>Chapter 6 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—6</li> </ul></li> <li><strong>APPLICATIONS OF TRIGONOMETRIC FUNCTIONS</strong> <ul> <li>7.1 The Law of Sines</li> <li>7.2 The Law of Cosines</li> <li>7.3 Areas of Polygons Using Trigonometry</li> <li>7.4 Vectors</li> <li>7.5 The Dot Product</li> <li>7.6 Polar Coordinates</li> <li>7.7 Polar Form of Complex Numbers; DeMoivre’s Theorem</li> <li>Chapter 7 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—7</li> </ul></li> <li><strong>SYSTEMS OF EQUATIONS AND INEQUALITIES</strong> <ul> <li>8.1 Systems of Linear Equations in Two Variables</li> <li>8.2 Systems of Linear Equations in Three Variables</li> <li>8.3 Partial-Fraction Decomposition</li> <li>8.4 Systems of Nonlinear Equations</li> <li>8.5 Systems of Inequalities</li> <li>8.6 Linear Programming</li> <li>Chapter 8 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—8</li> </ul></li> <li><strong>MATRICES AND DETERMINANTS</strong> <ul> <li>9.1 Matrices and Systems of Equations</li> <li>9.2 Matrix Algebra</li> <li>9.3 The Matrix Inverse</li> <li>9.4 Determinants and Cramer’s Rule</li> <li>Chapter 9 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—9</li> </ul></li> <li><strong>CONIC SECTIONS</strong> <ul> <li>10.1 Conic Sections: Overview</li> <li>10.2 The Parabola</li> <li>10.3 The Ellipse</li> <li>10.4 The Hyperbola</li> <li>Chapter 10 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—10</li> </ul></li> <li><strong>FURTHER TOPICS IN ALGEBRA</strong> <ul> <li>11.1 Sequences and Series</li> <li>11.2 Arithmetic Sequences; Partial Sums</li> <li>11.3 Geometric Sequences and Series</li> <li>11.4 Mathematical Induction</li> <li>11.5 The Binomial Theorem</li> <li>11.6 Counting Principles</li> <li>11.7 Probability</li> <li>Chapter 11 Review and Tests</li> <li>Review Exercises</li> <li>Practice Test A</li> <li>Practice Test B</li> <li>Cumulative Review Exercises Chapters P—11</li> </ul></li> </ol> <h4>Answers to Selected Exercises</h4> <h4>Credits</h4> <h4>Index</h4> <p></p>