Algebra & Trigonometry

<p><h3>Chapter R: A Review of Basic Concepts and Skills<h4>R-1The Language, Notation, and Numbers of Mathematics<h4>R-2Algebraic Expressions and the Properties of Real Numbers<h4>R-3Exponents, Scientific Notation, and a Review of Polynomials<h4>R-4Factoring Polynomials<h4>R-5Rational Expressions<h4>R-6Radicals and Rational Exponents<h3>Chapter 1: Equations and Inequalities</h3><h4>1-1Linear Equations, Formulas, and Problem Solving<h4>1-2Linear Inequalities in One Variable<h4>1-3Absolute Value Equations and Inequalities<h4>1-4Complex Numbers<h4>1-5Solving Quadratic Equations<h4>1-6Solving Other Types of Equations<h3>Chapter 2: Relations, Functions and Graphs</h3><h4>2-1Rectangular Coordinates; Graphing Circles and Relations<h4>2-2Graphs of Linear Equations<h4>2-3Linear Equations and Rates of Change<h4>2-4Functions, Notation, and Graphs of Functions<h4>2-5Analyzing the Graph of a Function<h4>2-6Toolbox Functions and Transformations<h4>2-7Piecewise-Defined Functions<h4>2-8The Algebra and Composition of Functions<h3>Chapter 3: Polynomial and Rational Functions</h3><h4>3-1Quadratic Functions and Applications<h4>3-2Synthetic Division; The Remainder and Factor Theorems<h4>3-3The Zeroes of Polynomial Functions<h4>3-4Graphing Polynomial Functions<h4>3-5Graphing Rational Functions<h4>3-6Additional Insights into Rational Functions<h4>3-7Polynomial and Rational Inequalities<h4>3-8Variation: Function Models in Action<h3>Chapter 4: Exponential and Logarithmic Functions</h3><h4>4-1One-to-One and Inverse Functions<h4>4-2Exponential Functions<h4>4-3Logarithms and Logarithmic Functions<h4>4-4Properties of Logarithms; Solving Exponential and Logarithmic Equations<h4>4-5Applications from Business, Finance, and Science<h3>Chapter 5: Introduction to Trigonometric Functions</h3><h4>5-1Angle Measure, Special Triangles, and Special Angles<h4>5-2The Trigonometry of Right Triangles <h4>5-3Trigonometry and the Coordinate Plane <h4>5-4Unit Circles and the Trigonometric of Real Numbers<h4>5-5Graphs of Sine and Cosine Functions; Cosecant and Secant Functions <h4>5-6Graphs of Tangent and Cotangent Functions <h4>5-7Transformations and Applications of Trigonometric Graphs<h3>Chapter 6: Trigonometric Identities, Inverses, and Equations</h3><h4>6-1Fundamental Identities and Families of Identities <h4>6-2Constructing and Verifying Identities <h4>6-3The Sum and Difference Identities <h4>6-4Double Angle, Half Angle & Product-to-Sum Identities<h4>6-5The Inverse Trigonometric Functions and Their Applications<h4>6-6Solving Basic Trigonometric Equations<h4>6-7General Trigonometric Equations and Applications<h3>Chapter 7: Applications of Trigonometry</h3><h4>7-1Oblique Triangles and the Law of Sines <h4>7-2The Law of Cosines; Area of a Triangle<h4>7-3Vectors and Vector Diagrams<h4>7-4Vector Applications and the Dot Product <h4>7-5Complex Numbers in Trigonometric Form <h4>7-6Demoivre’s Theorem and the Theorem on nth Roots <h3>Chapter 8: Systems of Equations and Inequalities</h3><h4>8-1Linear Systems in Two Variables with Applications<h4>8-2Linear Systems in Three Variables with Applications<h4>8-3Nonlinear Systems of Equations and Inequalities<h4>8-4Systems of Inequalities and Linear Programming<h3>Chapter 9: Matrices and Matrix Applications</h3><h4>9-1Solving Systems Using Matrices and Row Operations<h4>9-2The Algebra of Matrices<h4>9-3Solving Linear Systems Using Matrix Equations<h4>9-4Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More <h3>Chapter 10: Analytical Geometry and Conic Sections</h3><h4>10-1 Introduction to Analytic Geometry<h4>10-2 The Circle and the Ellipse<h4>10-3 The Hyperbola<h4>10-4 The Analytic Parabola<h4>10-5 Polar Coordinates, Equations, and Graphs<h4>10-6 More on Conic Sections: Rotation of Axes and Polar Form<h4>10-7 Parametric Equations and Graphs<h3>Chapter 11: Additional Topics in Algebra</h3><h4>11-1 Sequences and Series<h4>11-2 Arithmetic Sequences<h4>11-3 Geometric Sequences<h4>11-4 Mathematical Induction<h4>11-5 Counting Techniques<h4>11-6 Introduction to Probability<h4>11-7 The Binomial TheoremSummary and Concept Review<p><h4>APPENDICES<h5>A-1More on Synthetic Division<h5>A-2More on Matrices<h5>A-3Deriving the Equation of a Conic<h5>A-4Proof Positive - A Selection of Proofs from Algebra and Trigonometry