Algebra & Trigonometry (Coburn), 2nd EditionTable of ContentsChapter R: A Review of Basic Concepts and SkillsR-1 The Language, Notation, and Numbers of Mathematics R-2 Algebraic Expressions and the Properties of Real Numbers R-3 Exponents, Scientific Notation, and a Review of Polynomials R-4 Factoring Polynomials R-5 Rational Expressions R-6 Radicals and Rational Exponents Chapter 1: Equations and Inequalities 1-1 Linear Equations, Formulas, and Problem Solving 1-2 Linear Inequalities in One Variable 1-3 Absolute Value Equations and Inequalities 1-4 Complex Numbers 1-5 Solving Quadratic Equations 1-6 Solving Other Types of Equations Chapter 2: Relations, Functions and Graphs 2-1 Rectangular Coordinates; Graphing Circles and Relations 2-2 Graphs of Linear Equations 2-3 Linear Equations and Rates of Change 2-4 Functions, Notation, and Graphs of Functions 2-5 Analyzing the Graph of a Function 2-6 Toolbox Functions and Transformations 2-7 Piecewise-Defined Functions 2-8 The Algebra and Composition of Functions Chapter 3: Polynomial and Rational Functions 3-1 Quadratic Functions and Applications 3-2 Synthetic Division; The Remainder and Factor Theorems 3-3 The Zeroes of Polynomial Functions 3-4 Graphing Polynomial Functions 3-5 Graphing Rational Functions 3-6 Additional Insights into Rational Functions 3-7 Polynomial and Rational Inequalities 3-8 Variation: Function Models in Action Chapter 4: Exponential and Logarithmic Functions 4-1 One-to-One and Inverse Functions 4-2 Exponential Functions 4-3 Logarithms and Logarithmic Functions 4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations 4-5 Applications from Business, Finance, and Science 4-6 Business, Finance, and Science Applications Chapter 5: Introduction to Trigonometric Functions 5-1 Angle Measure, Special Triangles, and Special Angles 5-2 The Trigonometry of Right Triangles 5-3 Trigonometry and the Coordinate Plane 5-4 Unit Circles and the Trigonometric of Real Numbers 5-5 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions 5-6 Graphs of Tangent and Cotangent Functions 5-7 Transformations and Applications of Trigonometric Graphs Chapter 6: Trigonometric Identities, Inverses, and Equations 6-1 Fundamental Identities and Families of Identities 6-2 Constructing and Verifying Identities 6-3 The Sum and Difference Identities 6-4 Double Angle, Half Angle & Product-to-Sum Identities 6-5 The Inverse Trigonometric Functions and Their Applications 6-6 Solving Basic Trigonometric Equations 6-7 General Trigonometric Equations and Applications Chapter 7: Applications of Trigonometry 7-1 Oblique Triangles and the Law of Sines 7-2 The Law of Cosines; Area of a Triangle 7-3 Vectors and Vector Diagrams 7-4 Vector Applications and the Dot Product 7-5 Complex Numbers in Trigonometric Form 7-6 Demoivre’s Theorem and the Theorem on nth Roots Chapter 8: Systems of Equations and Inequalities 8-1 Linear Systems in Two Variables with Applications 8-2 Linear Systems in Three Variables with Applications 8-3 Nonlinear Systems of Equations and Inequalities 8-4 Systems of Inequalities and Linear Programming Chapter 9: Matrices and Matrix Applications 9-1 Solving Systems Using Matrices and Row Operations 9-2 The Algebra of Matrices 9-3 Solving Linear Systems Using Matrix Equations 9-4 Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More Chapter 10: Analytical Geometry and Conic Sections 10-1 Introduction to Analytic Geometry 10-2 The Circle and the Ellipse 10-3 The Hyperbola 10-4 The Analytic Parabola 10-5 Polar Coordinates, Equations, and Graphs 10-6 More on Conic Sections: Rotation of Axes and Polar Form 10-7 Parametric Equations and Graphs Chapter 11: Additional Topics in Algebra 11-1 Sequences and Series 11-2 Arithmetic Sequences 11-3 Geometric Sequences 11-4 Mathematical Induction 11-5 Counting Techniques 11-6 Introduction to Probability 11-7 The Binomial Theorem Summary and Concept Review APPENDICES A-1 More on Synthetic Division A-2 More on Matrices A-3 Deriving the Equation of a Conic A-4 Proof Positive - A Selection of Proofs from Algebra and Trigonometry |  |
