Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry, 5th edition

Michael Sullivan
, Michael Sullivan

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Precalculus: Concepts Through Functions, A Unit Circle 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.

ISBN-13: 9780138059088

Subject: Precalculus, College Algebra & Trigonometry

Category: Precalculus

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 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

5. Trigonometric Functions 

5.1 Angles, Arc Length, and Circular Motion 
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 Investigating Limits Using Tables and Graphs 
13.2 Algebraic 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

APPENDICES

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 
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