Algebra and Trigonometry, 12th edition

Applications Index

R. Review

• R.1 Real Numbers
• R.2 Algebra Essentials
• 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, Constant Rate Job Applications
• Chapter 1 Review, Test, and Projects

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
• Chapter 2 Review, Test, Cumulative Review, and Project

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
• Chapter 3 Review, Test, Cumulative Review, and Projects

4. Linear and Quadratic Functions

• 4.1 Properties of Linear Functions and Linear Models
• 4.2 Building Linear Models from Data
• 4.3 Quadratic Functions and Their Properties
• 4.4 Build Quadratic Models from Verbal Descriptions and from Data
• 4.5 Inequalities Involving Quadratic Functions
• Chapter 4 Review, Test, Cumulative Review, and Projects

5. Polynomial and Rational Functions

• 5.1 Polynomial Functions
• 5.2 Graphing Polynomials Functions; Models
• 5.3 Properties of Rational Functions
• 5.4 The Graph of a Rational Function
• 5.5 Polynomial and Rational Inequalities
• 5.6 The Real Zeros of a Polynomial Function
• 5.7 Complex Zeros; Fundamental Theorem of Algebra
• Chapter 5 Review, Test, Cumulative Review, and Projects

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
• Chapter 6 Review, Test, Cumulative Review, and Projects

7. Trigonometric Functions

• 7.1 Angles, Arc, Length, and Circular Motion
• 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
• Chapter 7 Review, Test, Cumulative Review, and Projects

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
• Chapter 8 Review, Test, Cumulative Review, and Projects

9. Applications of Trigonometric Functions

• 9.1 Applications Involving Right Triangles
• 9.2 The Law of Sines
• 9.3 The Law of Cosines
• 9.4 Area of a Triangle
• 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
• Chapter 9 Review, Test, Cumulative Revivew, and Projects

10. Polar Coordinates; Vectors

• 10.1 Polar Coordinates
• 10.2 Polar Equations and Graphs
• 10.3 The Complex Plane; De Moivre's Theorem
• 10.4 Vectors
• 10.5 The Dot Product
• Chapter 10 Review, Test, Cumulative Review, and Projects

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
• Chapter 11 Review, Test, Cumulative Review, and Projects

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
• Chapter 12 Review, Test, Cumulative Review, and Projects

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
• Chapter 13 Review, Test, Cumulative Review, and Projects

14. Counting and Probability

• 14.1 Counting
• 14.2 Permutations and Combinations
• 14.3 Probability
• Chapter 14 Review, Test, Cumulative Review, and Projects

Appendix: Graphing Utilities

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

Answers

Credits

Index