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

• Michael Sullivan Chicago State University
• Michael Sullivan Joliet Junior College
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Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry introduces functions at the beginning of the text, then introduces and develops a new function in every chapter. Known for connecting with students, esteemed authors Sullivan and Sullivan focus on the fundamentals (preparing for class, practicing with homework, and reviewing key concepts), which encourages you to master basic skills and develop the conceptual understanding needed for this and future courses. Graphing utility coverage is optional and can be adjusted for different course needs. The 5th Edition offers abundant new and updated features including new Challenge Problems, new Interactive Figure Exercises, and much more.

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