College Algebra and Trigonometry

PrefaceAcknowledgmentsTo the StudentChapter 1 The Foundations of Algebra 1.1 The Real Number System 1.2 The Real Number Line 1.3 Algebraic Expressions; Polynomials 1.4 Factoring 1.5 Rational Expressions 1.6 Integer Exponents 1.7 Rational Exponents and Radicals 1.8 Complex NumbersChapter 2 Equations and Inequalities 2.1 Linear Equations in One Unknown 2.2 Applications 2.3 Linear Inequalities 2.4 Absolute Value in Equations and Inequalities 2.5 The Quadratic Equation 2.6 Applications of Quadratic Equations 2.7 Second-Degree InequalitiesChapter 3 Functions 3.1 The Rectangular Coordinate System 3.2 Functions and Function Notation 3.3 Graphs of Functions 3.4 Linear Functions 3.5 Direct and Inverse Variation (Optional) 3.6 Combining Functions; Inverse FunctionsChapter 4 Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Fundamental Properties of Logarithms 4.4 Computing with Logarithms (Optional) 4.5 Exponential and Logarithmic EquationsChapter 5 The Trigonometric Functions 5.0 Review of Geometry 5.1 Angles and Their Measurement 5.2 The Sine, Cosine, and Tangent Functions 5.3 Values of Sine, Cosine, and Tangent 5.4 Graphs of Sine, Cosine, and Tangent 5.5 Secant, Cosecant, and Cotangent 5.6 The Inverse Trigonometric FunctionsChapter 6 Trigonometry: Measuring Triangles 6.1 Right Triangle Trigonometry 6.2 Applications of Right Triangle Trigonometry 6.3 Law of Cosines 6.4 Law of SinesChapter 7 Analytic Trigonometry 7.1 Trigonometric Identities 7.2 The Addition Formulas 7.3 Double- and Half-Angle Formulas 7.4 The Product-Sum Formulas 7.5 Trigonometric Equations 7.6 Trigonometry and Complex NumbersChapter 8 Analytic Geometry: The Conic Sections 8.1 Analytic Geometry 8.2 The Circle 8.3 The Parabola 8.4 The Ellipse and Hyperbola 8.5 Identifying the Conic SectionsChapter 9 Systems of Equations and Inequalities 9.1 Systems of Equations 9.2 Solving by Elimination 9.3 Applications 9.4 Systems of Linear Equations in Three Unknowns 9.5 Systems of Linear Inequalities 9.6 Linear Programming (Optional)Chapter 10 Matrices and Determinants 10.1 Matrices and Linear Systems 10.2 Matrix Operations and Applications (Optional) 10.3 Inverses of Matrices (Optional) 10.4 Determinants and Cramer's RuleChapter 11 Theory of Polynomials 11.1 Polynomial Division and Synthetic Division 11.2 The Remainder and Factor Theorems 11.3 Factors and Zeros 11.4 Real and Rational Zeros 11.5 Rational Functions and Their GraphsChapter 12 Topics in Algebra 12.1 Sequences and Sigma Notation 12.2 Arithmetic Sequences 12.3 Geometric Sequences 12.4 Mathematical Induction 12.5 The Binomial Theorem 12.6 Counting: Permutations and Combinations 12.7 ProbabilityTables AppendixAnswers to Odd-Numbered Exercises, and to Review Exercises and Progress TestsSolutions to Selected Review ExercisesIndex