Algebra & Trigonometry – Michael Sullivan – 9th Edition

R. Review
R.1 Real Numbers
R.2 Algebra Essential
R.3 Geometry Essentials
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 nth Roots; Rational Exponents

1. Equations and Inequalities
1.1 Linear Equations
1.2 Quadratic Equations
1.3 Complex Numbers; Quadratic Equations in the Complex Number System
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
1.5 Solving Inequalities
1.6 Equations and Inequalities Involving Absolute Value
1.7 Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Jobs Applications


2. Graphs
2.1 The Distance and Midpoint Formulas
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
2.3 Lines
2.4 Circles
2.5 Variation


3. Functions and Their Graphs
3.1 Functions
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewise-defined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions


4. Linear and Quadratic Functions
4.1 Linear Functions and Their Properties
4.2 Linear Models: Building Linear Functions from Data
4.3 Quadratic Functions and Their Properties
4.4 Building Quadratic Models from Data
4.5 Inequalities Involving Quadratic Functions


5. Polynomial and Rational Functions
5.1 Polynomial Functions and Models
5.2 Properties of Rational Functions
5.3 The Graph of a Rational Function
5.4 Polynomial and Rational Inequalities
5.5 The Real Zeros of a Polynomial Function
5.6 Complex Zeros: Fundamental Theorem of Algebra


6. Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 One-to-One Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Financial Models
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Models from Data

7. Trigonometric Functions
7.1 Angles and Their Measure
7.2 Right Triangle Trigonometry
7.3 Computing the Values of Trigonometric Functions of Acute Angles
7.4 Trigonometric Functions of Any Angle
7.5 Unit Circle Approach; Properties of the Trigonometric Functions
7.6 Graphs of the Sine and Cosine Functions
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
7.8 Phase Shift; Sinusoidal Curve Fitting


8. Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions
8.2 The Inverse Trigonometric Functions (continued)
8.3 Trigonometric Equations
8.4 Trigonometric Identities
8.5 Sum and Difference Formulas
8.6 Double-Angle and Half-Angle Formulas
8.7 Product-to-Sum and Sum-to-Product Formulas


9. Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles
9.2 Law of Sines
9.3 Law of Cosines
9.4 Area of a Triangle
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves


10. Polar Coordinates; Vectors
10.1 Polar Coordinates
10.2 Polar Equations and Graphs
10.3 The Complex Plane; DeMoivre’s Theorem
10.4 Vectors
10.5 The Dot Product


11. Analytic Geometry
11.1 Conics
11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola
11.5 Rotation of Axes; General Form of a Conic
11.6 Polar Equations of Conics
11.7 Plane Curves and Parametric Equations


12. Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination
12.2 Systems of Linear Equations: Matrices
12.3 Systems of Linear Equations: Determinants
12.4 Matrix Algebra
12.5 Partial Fraction Decomposition
12.6 Systems of Nonlinear Equations
12.7 Systems of Inequalities
12.8 Linear Programming


13. Sequences; Induction; The Binomial Theorem
13.1 Sequences
13.2 Arithmetic Sequences
13.3 Geometric Sequences; Geometric Series
13.4 Mathematical Induction
13.5 The Binomial Theorem


14. Counting and Probability
14.1 Sets and Counting
14.2 Permutations and Combinations
14.3 Probability

Appendix: Graphing Utilities

1. The Viewing Rectangle
2. Using a Graphing Utility to Graph Equations
3. Using a Graphing Utility to Graph Equations Locating Intercepts and Checking for Symmetry
4. Using a Graphing Utility to Solve Equations
5. Square Screens
6. Using a Graphing Utility to Graph Inequalities
7. Using a Graphing Utility to Solve Systems of Linear Equations
8. Using a Graphing Utility to Graph a Polar Equation
9. Using a Graphing Utility to Graph Parametric Equations