Algebra and Trigonometry

<h2>Table of Contents</h2> <div class="c-non-traditional-number-list_container"> <ol type="A" start="18"> <li><strong>Review</strong> <ul> <li>R.1 Real Numbers</li> <li>R.2 Algebra Essentials</li> <li>R.3 Geometry Essentials</li> <li>R.4 Polynomials</li> <li>R.5 Factoring Polynomials</li> <li>R.6 Synthetic Division</li> <li>R.7 Rational Expressions</li> <li>R.8 nth Roots; Rational Exponents</li> </ul></li> </ol> <ol> <li><strong>Equations and Inequalities</strong> <ul> <li>1.1 Linear Equations</li> <li>1.2 Quadratic Equations</li> <li>1.3 Complex Numbers; Quadratic Equations in the Complex Number System</li> <li>1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations</li> <li>1.5 Solving Inequalities</li> <li>1.6 Equations and Inequalities Involving Absolute Value</li> <li>1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications</li> </ul> <ul> <li>Chapter 1 Review, Test, and Projects</li> </ul></li> <li><strong>Graphs</strong> <ul> <li>2.1 The Distance and Midpoint Formulas</li> <li>2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry</li> <li>2.3 Lines</li> <li>2.4 Circles</li> <li>2.5 Variation</li> </ul> <ul> <li>Chapter 2 Review, Test, and Projects</li> </ul></li> <li><strong>Functions and Their Graphs</strong> <ul> <li>3.1 Functions</li> <li>3.2 The Graph of a Function</li> <li>3.3 Properties of Functions</li> <li>3.4 Library of Functions; Piecewise-defined Functions</li> <li>3.5 Graphing Techniques: Transformations</li> <li>3.6 Mathematical Models: Building Functions</li> </ul> <ul> <li>Chapter 3 Review, Test, and Projects</li> </ul></li> <li><strong>Linear and Quadratic Functions</strong> <ul> <li>4.1 Properties of Linear Functions and Linear Models</li> <li>4.2 Building Linear Models from Data</li> <li>4.3 Quadratic Functions and Their Properties</li> <li>4.4 Build Quadratic Models from Verbal Descriptions and from Data</li> <li>4.5 Inequalities Involving Quadratic Functions</li> </ul> <ul> <li>Chapter 4 Review, Test, and Projects</li> </ul></li> <li><strong>Polynomial and Rational Functions</strong> <ul> <li>5.1 Polynomial Functions</li> <li>5.2 Graphing Polynomials Functions; Models</li> <li>5.3 Properties of Rational Functions</li> <li>5.4 The Graph of a Rational Function</li> <li>5.5 Polynomial and Rational Inequalities</li> <li>5.6 The Real Zeros of a Polynomial Function</li> </ul> <ul> <li>Chapter 5 Review, Test, and Projects</li> </ul></li> <li><strong>Exponential and Logarithmic Functions</strong> <ul> <li>6.1 Composite Functions</li> <li>6.2 One-to-One Functions; Inverse Functions</li> <li>6.3 Exponential Functions</li> <li>6.4 Logarithmic Functions</li> <li>6.5 Properties of Logarithms</li> <li>6.6 Logarithmic and Exponential Equations</li> <li>6.7 Financial Models</li> <li>6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models</li> <li>6.9 Building Exponential, Logarithmic, and Logistic Models from Data</li> </ul> <ul> <li>Chapter 6 Review, Test, and Projects</li> </ul></li> <li><strong>Trigonometric Functions</strong> <ul> <li>7.1 Angles, Arc, Length, and Circular Motion</li> <li>7.2 Right Triangle Trigonometry</li> <li>7.3 Computing the Values of Trigonometric Functions of Acute Angles</li> <li>7.4 Trigonometric Functions of Any Angle</li> <li>7.5 Unit Circle Approach; Properties of the Trigonometric Functions</li> <li>7.6 Graphs of the Sine and Cosine Functions</li> <li>7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions</li> <li>7.8 Phase Shift; Sinusoidal Curve Fitting</li> </ul> <ul> <li>Chapter 7 Review, Test, and Projects</li> </ul></li> <li><strong>Analytic Trigonometry</strong> <ul> <li>8.1 The Inverse Sine, Cosine, and Tangent Functions</li> <li>8.2 The Inverse Trigonometric Functions (Continued)</li> <li>8.3 Trigonometric Equations</li> <li>8.4 Trigonometric Identities</li> <li>8.5 Sum and Difference Formulas</li> <li>8.6 Double-angle and Half-angle Formulas</li> <li>8.7 Product-to-Sum and Sum-to-Product Formulas</li> </ul> <ul> <li>Chapter 8 Review, Test, and Projects</li> </ul></li> <li><strong>Applications of Trigonometric Functions</strong> <ul> <li>9.1 Applications Involving Right Triangles</li> <li>9.2 The Law of Sines</li> <li>9.3 The Law of Cosines</li> <li>9.4 Area of a Triangle</li> <li>9.5 Simple Harmonic Motion; Damped Motion; Combining Waves</li> </ul> <ul> <li>Chapter 9 Review, Test, and Projects</li> </ul></li> <li><strong>Polar Coordinates; Vectors</strong> <ul> <li>10.1 Polar Coordinates</li> <li>10.2 Polar Equations and Graphs</li> <li>10.3 The Complex Plane; De Moivre’s Theorem</li> <li>10.4 Vectors</li> <li>10.5 The Dot Product</li> </ul> <ul> <li>Chapter 10 Review, Test, and Projects</li> </ul></li> <li><strong>Analytic Geometry</strong> <ul> <li>11.1 Conics</li> <li>11.2 The Parabola</li> <li>11.3 The Ellipse</li> <li>11.4 The Hyperbola</li> <li>11.5 Rotation of Axes; General Form of a Conic</li> <li>11.6 Polar Equations of Conics</li> <li>11.7 Plane Curves and Parametric Equations</li> </ul> <ul> <li>Chapter 11 Review, Test, and Projects</li> </ul></li> <li><strong>Systems of Equations and Inequalities</strong> <ul> <li>12.1 Systems of Linear Equations: Substitution and Elimination</li> <li>12.2 Systems of Linear Equations: Matrices</li> <li>12.3 Systems of Linear Equations: Determinants</li> <li>12.4 Matrix Algebra</li> <li>12.5 Partial Fraction Decomposition</li> <li>12.6 Systems of Nonlinear Equations</li> <li>12.7 Systems of Inequalities</li> <li>12.8 Linear Programming</li> </ul> <ul> <li>Chapter 12 Review, Test, and Projects</li> </ul></li> <li><strong>Sequences; Induction; the Binomial Theorem</strong> <ul> <li>13.1 Sequences</li> <li>13.2 Arithmetic Sequences</li> <li>13.3 Geometric Sequences; Geometric Series</li> <li>13.4 Mathematical Induction</li> <li>13.5 The Binomial Theorem</li> </ul> <ul> <li>Chapter 13 Review, Test, and Projects</li> </ul></li> <li><strong>Counting and Probability</strong> <ul> <li>14.1 Counting</li> <li>14.2 Permutations and Combinations</li> <li>14.3 Probability</li> </ul> <ul> <li>Chapter 14 Review, Test, and Projects</li> </ul></li> </ol> <h3>Appendix: Graphing Utilities</h3> <ul> <li>A.1 The Viewing Rectangle</li> <li>A.2 Using a Graphing Utility to Graph Equations</li> <li>A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry</li> <li>A.4 Using a Graphing Utility to Solve Equations</li> <li>A.5 Square Screens</li> <li>A.6 Using a Graphing Utility to Graph Inequalities</li> <li>A.7 Using a Graphing Utility to Solve Systems of Linear Equations</li> <li>A.8 Using a Graphing Utility to Graph a Polar Equation</li> <li>A.9 Using a Graphing Utility to Graph Parametric Equations</li> </ul> <h4 class="h5">Answers</h4> <h4 class="h5">Credits</h4> <h4 class="h5">Index</h4> </div>