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

  • Michael Sullivan, 
  • Michael Sullivan

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Hallmark features of this title

  • Just-in-time review starts each section: Preparing for This Section lists earlier concepts that will be useful for the section ahead. Now Work "Are You Prepared?" problems help students assess their understanding.
  • Now Work problems: If students get stuck during homework, they can look for the closest Now Work problem and refer back to the related example.
  • Step-by-Step, Annotated Examples have detailed intermediate steps with annotations to help students see nuances.
  • Assess Your Understanding at the end of every section contains a variety of problems for skill mastery.
  • Skill Development problems are organized by difficulty and correlated to section examples.
  • Graphical problems  use graphs in a variety of ways to supplement students’ analytical understanding.

Published by Pearson (September 29th 2023) - Copyright © 2024

ISBN-13: 9780137979462

Subject: Precalculus, College Algebra & Trigonometry

Category: Precalculus

Table of contents

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

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