Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, 4th edition

  • Michael Sullivan

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Overview

Precalculus introduces calculus functions at the start of the text and continues to present and develop concepts in every chapter. Focusing on the fundamentals -- preparing for class, practice with homework, and reviewing key concepts, the author encourages you to master the basic math skills needed for this and future courses.

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

ISBN-13: 9780137399581

Subject: Precalculus, College Algebra & Trigonometry

Category: Precalculus

Table of contents

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
  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: Constructing 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
    • Chapter Projects
    • Cumulative Review
  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
    • Chapter Projects
    • Cumulative Review
  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
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  5. Trigonometric Functions
    • 5.1 Angles and Their Measure
    • 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
    • Chapter Projects
    • Cumulative Review
  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
    • Chapter Projects
    • Cumulative Review
  7. Applications of Trigonometric Functions
    • 7.1 Right Triangle Trigonometry; 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
    • Chapter Projects
    • Cumulative Review
  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
    • Chapter Projects
    • Cumulative Review
  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
    • Chapter Projects
    • Cumulative Review
  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
    • Chapter Projects
    • Cumulative Review
  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
    • Chapter Projects
    • Cumulative Review
  12. Counting and Probability
    • 12.1 Counting
    • 12.2 Permutations and Combinations
    • 12.3 Probability
    • Chapter Review
    • Chapter Test
    • Chapter Projects
    • Cumulative Review
  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 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

Answers

Index

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