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

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry, 4th edition

  • Michael Sullivan

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Overview

In the Concepts Through Functions Series, authors Sullivan and Sullivan focus you on the fundamentals -- preparing for class, practice with homework, and reviewing key concepts -- encouraging you to master basic skills and develop the conceptual understanding needed for this and future courses.

Published by Pearson (January 25th 2021) - Copyright © 2019

ISBN-13: 9780137399635

Subject: Precalculus, College Algebra & Trigonometry

Category: Precalculus

Table of contents

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 Mathematical Models: Building Functions
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 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

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 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

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