Published by Pearson (May 8, 2019) © 2019
For courses in Precalculus.
Known for their ability to connect with students, Sullivan and Sullivan focus on the fundamentals (preparing for class, practice with homework, reviewing key concepts), encouraging the conceptual understanding and mastery of basic skills needed for this and future courses. Part of the Concepts Through Functions Series, Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry, 4th Edition introduces functions at the start and maintains a continuous theme by introducing/developing a new function in every chapter. Graphing utility coverage is optional and can be included at the instructor's discretion.
Study Skills for Mathematics
SS1How Learning Math is Different
SS2The Growth Mindset and Grit
SS3Resources Available for Help
SS4Time Management
SS5How to be An Effective Listener and How to Take Notes
SS6How to do Math Homework the Right Way
SS7How to Read a Math Book
SS8How to Study for a Math Exam
SS9Overcoming Math and Test Anxiety
Elementary Algebra Review
R.1 Sets and Classifications of Numbers
R.2 Properties of Real Numbers
R.3 Perform Operations on Rational Numbers
R.4 Order of Operations
R.5 Algebraic Expressions
R.6 Square Roots
R.8 Geometry Essentials
R.9 Laws of Exponents
R.10 Adding and Subtracting Polynomials
R.11 Multiplying Polynomials
Preparing for Chapter F
F.P1 Linear Equations in One Variable
F.P2 Greatest Common Factor; Factoring by Grouping
F.P3 More Factoring
F.P4 Polynomial Equations
F.P5 Solving Quadratic Equations by Completing the Square
Chapter 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
Preparing for Chapter 1
1.P1 Linear Inequalities in One Variable
1.P2 nth Roots
1.P3 An Introduction to Problem Solving
Chapter 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 Mathematical Models: Building Functions
1.7 Building Mathematical Models Using Variation
Preparing for Chapter 2
2.P1 Factoring Trinomials Where the Leading Coefficient is Not One
Factor trinomials for the form ax2 + bx + c, a ≠ 1
2.P2 The Complex Number System
Solve quadratic equations using the Square Root Property
2.P3 Solving Quadratic Equations by the Quadratic Formula
2.P4 Solving Equations Quadratic in Form
2.P5 Compound Inequalities
Chapter 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
Preparing for Chapter 3
3.P1 Factoring
3.P2 Dividing Polynomials; Synthetic Division
3.P3 Multiplying and Dividing Rational Expressions
3.P4 Adding and subtracting rational expressions
3.P5 Complex Rational Expressions
3.P6 Rational Equations
Chapter 3. 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
Preparing for Chapter 4
4.P1 Rational Exponents
4.P2 Simplifying Expressions Using the Laws of Exponents
4.P3 Simplifying Radical Expressions Using Properties of Radicals
4.P4 Adding, Subtracting, and Multiplying Radical Expressions
4.P5 Rationalizing Radical Expressions
Chapter 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 Compound Interest
4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay
4.9 Building Exponential, Logarithmic, and Logistic Functions from Data
5. 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
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 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
8. 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
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 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 B1
B.2 Using a Graphing Utility to Graph Equations B3
B.3 Using a Graphing Utility to Locate Intercepts and Check
for Symmetry B5
B.4 Using a Graphing Utility to Solve Equations B6
B.5 Square Screens B8
B.6 Using a Graphing Utility to Graph Inequalities B9
B.7 Using a Graphing Utility to Solve Systems of Linear Equations B9
B.8 Using a Graphing Utility to Graph a Polar Equation B11
B.9 Using a Graphing Utility to Graph Parametric Equations B11
Answers
Photo Credits
Index
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!
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