<div class="c-un-numbered-headers-and-contents-list__container"> <h3>BRIEF TABLE OF CONTENTS</h3> <ul> <li>NOTE: Both brief and comprehensive tables of contents are listed below.</li> </ul> <br> <h4>Review Chapter</h4> <ol> <li>Equations, Inequalities, and Applications</li> <li>The Rectangular Coordinate System, Lines, and Circles</li> <li>Functions</li> <li>Polynomial and Rational Functions</li> <li>Exponential and Logarithmic Functions and Equations</li> <li>An Introduction to Trigonometric Functions</li> <li>The Graphs of Trigonometric Functions</li> <li>Trigonometric Identities, Formulas, and Equations</li> <li>Applications of Trigonometry</li> <li>Polar Equations, Complex Numbers, and Vectors</li> <li>Conic Sections and Parametric Equations</li> <li>Systems of Equations and Inequalities</li> <li>Matrices</li> <li>Sequences and Series; Counting and Probability</li> </ol> <h4>Appendices</h4> <ul> <li>A. Degree, Minute, Second Form and Degree Decimal Form</li> <li>B. Conic Section Proofs</li> </ul> <h3>COMPREHENSIVE TABLE OF CONTENTS</h3> <ul> <li><strong>R. Review Chapter</strong> <ul> <li>R.1 Real Numbers</li> <li>R.2 The Order of Operations and Algebraic Expressions</li> <li>R.3 The Laws of Exponents; Radicals</li> <li>R.4 Polynomials</li> <li>R.5 Operations with Radicals (New Section)</li> <li>R.6 Factoring Polynomials</li> <li>R.7 Rational Expressions</li> </ul> </li> </ul> <ol> <li><strong>Equations, Inequalities, and Applications</strong> <ul> <li>1.1 Linear and Rational Equations</li> <li>1.2 Applications of Linear Equations and Rational Equation</li> <li>1.3 Complex Numbers</li> <li>1.4 Quadratic Equations</li> <li>1.5 Applications of Quadratic Equations</li> <li>1.6 Other Types of Equations</li> <li>1.7 Linear Inequalities in One Variable</li> <li>1.8 Absolute Value Equations and Inequalities</li> <li>1.9 Polynomial and Rational Inequalities</li> </ul> </li> <li><strong>The Rectangular Coordinate System, Lines, and Circles</strong> <ul> <li>2.1 The Rectangular Coordinate System</li> <li>2.2 Circles</li> <li>2.3 Lines</li> <li>2.4 Parallel and Perpendicular Lines</li> </ul> </li> <li><strong>Functions</strong> <ul> <li>3.1 Relations and Functions</li> <li>3.2 Properties of a Function’s Graph</li> <li>3.3 Graphs of Basic Functions; Piecewise Functions</li> <li>3.4 Transformations of Functions</li> <li>3.5 The Algebra of Functions; Composite Functions</li> <li>3.6 One-to-One Functions; Inverse Functions</li> </ul> </li> <li><strong>Polynomial and Rational Functions</strong> <ul> <li>4.1 Quadratic Functions</li> <li>4.2 Applications and Modeling of Quadratic Functions</li> <li>4.3 The Graphs of Polynomial Functions</li> <li>4.4 Synthetic Division; The Remainder and Factor Theorems</li> <li>4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra</li> <li>4.6 Rational Functions and Their Graphs</li> <li>4.7 Variation</li> </ul> </li> <li><strong>Exponential and Logarithmic Functions and Equations</strong> <ul> <li>5.1 Exponential Functions</li> <li>5.2 Logarithmic Functions</li> <li>5.3 Properties of Logarithms</li> <li>5.4 Exponential and Logarithmic Equations</li> <li>5.5 Applications of Exponential and Logarithmic Functions</li> </ul> </li> <li><strong>An Introduction to Trigonometric Functions</strong> <ul> <li>6.1 An Introduction to Angles: Degree and Radian Measure</li> <li>6.2 Applications of Radian Measure</li> <li>6.3 Triangles</li> <li>6.4 Right Triangle Trigonometry</li> <li>6.5 Trigonometric Functions of General Angles</li> <li>6.6 The Unit Circle</li> </ul> </li> <li><strong>The Graphs of Trigonometric Functions</strong> <ul> <li>7.1 The Graphs of Sine and Cosine</li> <li>7.2 More on Graphs of Sine and Cosine; Phase Shift</li> <li>7.3 The Graphs of the Tangent, Cotangent , Cosecant, and Secant Functions</li> <li>7.4 Inverse Trigonometric Functions I</li> <li>7.5 Inverse Trigonometric Functions II</li> </ul> </li> <li><strong>Trigonometric Identities, Formulas, and Equations</strong> <ul> <li>8.1 Trigonometric Identities</li> <li>8.2 The Sum and Difference Formulas</li> <li>8.3 The Double-Angle and Half-Angle Formulas</li> <li>8.4 The Product-to-Sum and Sum-to-Product Formulas</li> <li>8.5 Trigonometric Equations</li> </ul> </li> <li><strong>Applications of Trigonometry</strong> <ul> <li>9.1 Right Triangle Applications</li> <li>9.2 The Law of Sines</li> <li>9.3 The Law of Cosines</li> <li>9.4 Area of Triangles</li> </ul> </li> <li><strong>Polar Equations, Complex Numbers, and Vectors</strong> <ul> <li>10.1 Polar Coordinates and Polar Equations</li> <li>10.2 Graphing Polar Equations</li> <li>10.3 Complex Numbers in Polar Form; DeMoivre’s Theorem</li> <li>10.4 Vectors</li> <li>10.5 The Dot Product</li> </ul> </li> <li><strong>Conic Sections and Parametric Equations</strong> <ul> <li>11.1 Introduction to Conic Sections</li> <li>11.2 The Parabola</li> <li>11.3 The Ellipse</li> <li>11.4 The Hyperbola</li> <li>11.5 Conic Sections in Polar Form</li> <li>11.6 Parametric Equations</li> </ul> </li> <li><strong>Systems of Equations and Inequalities</strong> <ul> <li>12.1 Solving Systems of Linear Equations in Two Variables</li> <li>12.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method</li> <li>12.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination</li> <li>12.4 Partial Fraction Decomposition</li> <li>12.5 Systems of Nonlinear Equations</li> <li>12.6 Systems of Inequalities</li> </ul> </li> <li><strong>Matrices</strong> <ul> <li>13.1 Matrix Operations</li> <li>13.2 Inverses of Matrices and Matrix Equations</li> <li>13.3 Determinants and Cramer’s Rule</li> </ul> </li> <li><strong>Sequences and Series; Counting and Probability</strong> <ul> <li>14.1 Introduction to Sequences and Series</li> <li>14.2 Arithmetic Sequences and Series</li> <li>14.3 Geometric Sequences and Series</li> <li>14.4 The Binomial Theorem</li> <li>14.5 Mathematical Induction</li> <li>14.6 The Theory of Counting</li> <li>14.7 An Introduction to Probability</li> </ul> </li> </ol> <h4>Appendices</h4> <ul> <li>A. Degree, Minute, Second Form and Degree Decimal Form</li> <li>B. Conic Section Proofs</li> </ul> </div>