Precalculus (4^th Ed.) Concepts Through Functions, A Unit Circle Approach to Trigonometry

For courses in precalculus.

Ties concepts together using a functions approach

The Concepts Through Functions Series introduces functions at the start of each text, and maintains a continuous theme by introducing/developing a new function in every chapter.

Known for their ability to connect with today?s students, acclaimed authors Sullivan and Sullivan focus on the fundamentals ? preparing for class, practice with homework, and reviewing key concepts ? encouraging students to master basic skills and develop the conceptual understanding needed for this and future courses. Graphing utility coverage is optional, and can be included at the discretion of each instructor based on course needs.

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Table of Contents

1. 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
2. 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 Mathematical Models: Building Functions
   • 1.7 Building Mathematical Models Using Variation
   • Chapter Review
   • Chapter Test
   • Chapter Projects
3. 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
4. Polynomial and Rational Functions
   • 3.1 Polynomial Functions and Models
   • 3.2 The Real Zeros of a Polynomial Function
   • 3.3 Complex Zeros; Fundamental Theorem of Algebra
   • 3.4 Properties of Rational Functions
   • 3.5 The Graph of a Rational Function
   • 3.6 Polynomial and Rational Inequalities
   • Chapter Review
   • Chapter Test
   • Cumulative Review
   • Chapter Projects
5. 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 Models; 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
6. Trigonometric Functions
   • 5.1 Angles and Their Measure
   • 5.2 Trigonometric Functions: Unit Circle Approach
   • 5.3 Properties of the Trigonometric Functions
   • 5.4 Graphs of the Sine and Cosine Functions
   • 5.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
   • 5.6 Phase Shift; Sinusoidal Curve Fitting
   • Chapter Review
   • Chapter Test
   • Cumulative Review
   • Chapter Projects
7. 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
8. Applications of Trigonometric Functions
   • 7.1 Right Triangle Trigonometry; Applications
   • 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
9. Polar Coordinates; Vectors
   • 8.1 Polar Coordinates
   • 8.2 Polar Equations and Graphs
   • 8.3 The Complex Plane; De Moivre’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
10. 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
11. 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
12. 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
13. Counting and Probability
    • 12.1 Counting
    • 12.2 Permutations and Combinations
    • 12.3 Probability
    • Chapter Review
    • Chapter Test
    • Cumulative Review
    • Chapter Projects
14. A Preview of Calculus: The Limit, Derivative, and Integral of a Function
    • 13.1 Finding Limits Using Tables and Graphs
    • 13.2 Algebra Techniques for Finding Limits
    • 13.3 One-sided Limits; Continuous Functions
    • 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 Job Applications
• 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

Photo Credits

Index

About our authors

Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has 4 children; the 2 oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son Mike Sullivan, III co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than 10 books. He owns a travel agency and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where he enjoys gardening.

Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series which he writes with his father, Michael Sullivan.

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportunity to do both at the same time!

Hallmark features of this title

• Just-in-time review begins all sections to prepare students for the topics ahead.
• Preparing for This Section lists previously learned concepts with page references that will be useful in the section ahead.
• Now Work "Are You Prepared?" problems at the start of each exercise set help students check their preparedness for the section ahead.
• Within each section, students get guidance to help them master material and develop problem-solving skills.
• Assess Your Understanding at the end of every section offers a variety of problems to help students master skills.
• DWR (Discussion, Writing and Research) problems are marked by an icon and red numbers. They support class discussion, verbalization of mathematical ideas, and writing and research projects.