Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, 5th edition

Applications Index

F. Foundations: A Prelude to Functions

• F.1 The Distance and Midpoint Formulas
• F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
• F.3 Lines
• F.4 Circles
• Chapter Project

1. Functions and Their Graphs

• 1.1 Functions
• 1.2 The Graph of a Function
• 1.3 Properties of Functions
• 1.4 Library of Functions; Piecewise-defined Functions
• 1.5 Graphing Techniques: Transformations
• 1.6 Building Mathematical Models from Verbal Descriptions
• 1.7 Building Mathematical Models Using Variation
• Chapter Review
• Chapter Test
• Chapter Projects

2. Linear and Quadratic Functions

• 2.1 Properties of Linear Functions and Linear Models
• 2.2 Building Linear Models from Data
• 2.3 Quadratic Functions and Their Zeros
• 2.4 Properties of Quadratic Functions
• 2.5 Inequalities Involving Quadratic Functions
• 2.6 Building Quadratic Models from Verbal Descriptions and from Data
• 2.7 Complex Zeros of a Quadratic Function
• 2.8 Equations and Inequalities Involving the Absolute Value Function
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

3. Polynomial and Rational Functions

• 3.1 Polynomial Functions
• 3.2 Graphing Polynomial Functions; Models
• 3.3 The Real Zeros of a Polynomial Function
• 3.4 Complex Zeros; Fundamental Theorem of Algebra
• 3.5 Properties of Rational Functions
• 3.6 The Graph of a Rational Function
• 3.7 Polynomial and Rational Inequalities
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

4. Exponential and Logarithmic Functions

• 4.1 Composite Functions
• 4.2 One-to-One Functions; Inverse Functions
• 4.3 Exponential Functions
• 4.4 Logarithmic Functions
• 4.5 Properties of Logarithms
• 4.6 Logarithmic and Exponential Equations
• 4.7 Financial Models
• 4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay Models
• 4.9 Building Exponential, Logarithmic, and Logistic Models from Data
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

5. Trigonometric Functions

• 5.1 Angles, Arc Length, and Circular Motion
• 5.2 Right Triangle Trigonometry
• 5.3 Computing the Values of Trigonometric Functions of Acute Angles
• 5.4 Trigonometric Functions of Any Angle
• 5.5 Unit Circle Approach; Properties of the Trigonometric Functions
• 5.6 Graphs of the Sine and Cosine Functions
• 5.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
• 5.8 Phase Shift; Sinusoidal Curve Fitting
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

6. Analytic Trigonometry

• 6.1 The Inverse Sine, Cosine, and Tangent Functions
• 6.2 The Inverse Trigonometric Functions (Continued)
• 6.3 Trigonometric Equations
• 6.4 Trigonometric Identities
• 6.5 Sum and Difference Formulas
• 6.6 Double-angle and Half-angle Formulas
• 6.7 Product-to-Sum and Sum-to-Product Formulas
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

7. Applications of Trigonometric Functions

• 7.1 Applications Involving Right Triangles
• 7.2 The Law of Sines
• 7.3 The Law of Cosines
• 7.4 Area of a Triangle
• 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

8. Polar Coordinates; Vectors

• 8.1 Polar Coordinates
• 8.2 Polar Equations and Graphs
• 8.3 The Complex Plane; DeMoivre's Theorem
• 8.4 Vectors
• 8.5 The Dot Product
• 8.6 Vectors in Space
• 8.7 The Cross Product
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

9. Analytic Geometry

• 9.1 Conics
• 9.2 The Parabola
• 9.3 The Ellipse
• 9.4 The Hyperbola
• 9.5 Rotation of Axes; General Form of a Conic
• 9.6 Polar Equations of Conics
• 9.7 Plane Curves and Parametric Equations
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

10. Systems of Equations and Inequalities

• 10.1 Systems of Linear Equations: Substitution and Elimination
• 10.2 Systems of Linear Equations: Matrices
• 10.3 Systems of Linear Equations: Determinants
• 10.4 Matrix Algebra
• 10.5 Partial Fraction Decomposition
• 10.6 Systems of Nonlinear Equations
• 10.7 Systems of Inequalities
• 10.8 Linear Programming
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

11. Sequences; Induction; the Binomial Theorem

• 11.1 Sequences
• 11.2 Arithmetic Sequences
• 11.3 Geometric Sequences; Geometric Series
• 11.4 Mathematical Induction
• 11.5 The Binomial Theorem
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

12. Counting and Probability

• 12.1 Counting
• 12.2 Permutations and Combinations
• 12.3 Probability
• Chapter Review
• Chapter Test
• Cumulative Review
• Chapter Projects

13. A Preview of Calculus: The Limit, Derivative, and Integral of a Function

• 13.1 Investigating Limits Using Tables and Graphs
• 13.2 Algebra Techniques for Finding Limits
• 13.3 One-sided Limits; Continuity
• 13.4 The Tangent Problem; The Derivative
• 13.5 The Area Problem; The Integral
• Chapter Review
• Chapter Test
• Chapter Projects

Appendix A. Review

• A.1 Algebra Essentials
• A.2 Geometry Essentials
• A.3 Polynomials
• A.4 Factoring Polynomials
• A.5 Synthetic Division
• A.6 Rational Expressions
• A.7 nth Roots; Rational Exponents
• A.8 Solving Equations
• A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs
• A.10 Interval Notation; Solving Inequalities
• A.11 Complex Numbers

Appendix B. Graphing Utilities

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

Answers

Index