Description

Book Synopsis


Table of Contents
Table of Contents

  1. Review
    • R.1 Real Numbers
    • R.2 Algebra Essentials
    • R.3 Geometry Essentials
    • R.4 Polynomials
    • R.5 Factoring Polynomials
    • R.6 Synthetic Division
    • R.7 Rational Expressions
    • R.8 nth Roots; Rational Exponents
  2. Equations and Inequalities
    • 1.1 Linear Equations
    • 1.2 Quadratic Equations
    • 1.3 Complex Numbers; Quadratic Equations in the Complex Number System
    • 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
    • 1.5 Solving Inequalities
    • 1.6 Equations and Inequalities Involving Absolute Value
    • 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
    • Chapter 1 Review, Test, and Projects
  3. Graphs
    • 2.1 The Distance and Midpoint Formulas
    • 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
    • 2.3 Lines
    • 2.4 Circles
    • 2.5 Variation
    • Chapter 2 Review, Test, and Projects
  4. Functions and Their Graphs
    • 3.1 Functions
    • 3.2 The Graph of a Function
    • 3.3 Properties of Functions
    • 3.4 Library of Functions; Piecewise-defined Functions
    • 3.5 Graphing Techniques: Transformations
    • 3.6 Mathematical Models: Building Functions
    • Chapter 3 Review, Test, and Projects
  5. Linear and Quadratic Functions
    • 4.1 Properties of Linear Functions and Linear Models
    • 4.2 Building Linear Models from Data
    • 4.3 Quadratic Functions and Their Properties
    • 4.4 Build Quadratic Models from Verbal Descriptions and from Data
    • 4.5 Inequalities Involving Quadratic Functions
    • Chapter 4 Review, Test, and Projects
  6. Polynomial and Rational Functions
    • 5.1 Polynomial Functions
    • 5.2 Graphing Polynomials Functions; Models
    • 5.3 Properties of Rational Functions
    • 5.4 The Graph of a Rational Function
    • 5.5 Polynomial and Rational Inequalities
    • 5.6 The Real Zeros of a Polynomial Function
    • Chapter 5 Review, Test, and Projects
  7. Exponential and Logarithmic Functions
    • 6.1 Composite Functions
    • 6.2 One-to-One Functions; Inverse Functions
    • 6.3 Exponential Functions
    • 6.4 Logarithmic Functions
    • 6.5 Properties of Logarithms
    • 6.6 Logarithmic and Exponential Equations
    • 6.7 Financial Models
    • 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
    • 6.9 Building Exponential, Logarithmic, and Logistic Models from Data
    • Chapter 6 Review, Test, and Projects
  8. Trigonometric Functions
    • 7.1 Angles, Arc, Length, and Circular Motion
    • 7.2 Right Triangle Trigonometry
    • 7.3 Computing the Values of Trigonometric Functions of Acute Angles
    • 7.4 Trigonometric Functions of Any Angle
    • 7.5 Unit Circle Approach; Properties of the Trigonometric Functions
    • 7.6 Graphs of the Sine and Cosine Functions
    • 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
    • 7.8 Phase Shift; Sinusoidal Curve Fitting
    • Chapter 7 Review, Test, and Projects
  9. Analytic Trigonometry
    • 8.1 The Inverse Sine, Cosine, and Tangent Functions
    • 8.2 The Inverse Trigonometric Functions (Continued)
    • 8.3 Trigonometric Equations
    • 8.4 Trigonometric Identities
    • 8.5 Sum and Difference Formulas
    • 8.6 Double-angle and Half-angle Formulas
    • 8.7 Product-to-Sum and Sum-to-Product Formulas
    • Chapter 8 Review, Test, and Projects
  10. Applications of Trigonometric Functions
    • 9.1 Applications Involving Right Triangles
    • 9.2 The Law of Sines
    • 9.3 The Law of Cosines
    • 9.4 Area of a Triangle
    • 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
    • Chapter 9 Review, Test, and Projects
  11. Polar Coordinates; Vectors
    • 10.1 Polar Coordinates
    • 10.2 Polar Equations and Graphs
    • 10.3 The Complex Plane; De Moivre’s Theorem
    • 10.4 Vectors
    • 10.5 The Dot Product
    • Chapter 10 Review, Test, and Projects
  12. Analytic Geometry
    • 11.1 Conics
    • 11.2 The Parabola
    • 11.3 The Ellipse
    • 11.4 The Hyperbola
    • 11.5 Rotation of Axes; General Form of a Conic
    • 11.6 Polar Equations of Conics
    • 11.7 Plane Curves and Parametric Equations
    • Chapter 11 Review, Test, and Projects
  13. Systems of Equations and Inequalities
    • 12.1 Systems of Linear Equations: Substitution and Elimination
    • 12.2 Systems of Linear Equations: Matrices
    • 12.3 Systems of Linear Equations: Determinants
    • 12.4 Matrix Algebra
    • 12.5 Partial Fraction Decomposition
    • 12.6 Systems of Nonlinear Equations
    • 12.7 Systems of Inequalities
    • 12.8 Linear Programming
    • Chapter 12 Review, Test, and Projects
  14. Sequences; Induction; the Binomial Theorem
    • 13.1 Sequences
    • 13.2 Arithmetic Sequences
    • 13.3 Geometric Sequences; Geometric Series
    • 13.4 Mathematical Induction
    • 13.5 The Binomial Theorem
    • Chapter 13 Review, Test, and Projects
  15. Counting and Probability
    • 14.1 Counting
    • 14.2 Permutations and Combinations
    • 14.3 Probability
    • Chapter 14 Review, Test, and Projects
Appendix: Graphing Utilities
  • A.1 The Viewing Rectangle
  • A.2 Using a Graphing Utility to Graph Equations
  • A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
  • A.4 Using a Graphing Utility to Solve Equations
  • A.5 Square Screens
  • A.6 Using a Graphing Utility to Graph Inequalities
  • A.7 Using a Graphing Utility to Solve Systems of Linear Equations
  • A.8 Using a Graphing Utility to Graph a Polar Equation
  • A.9 Using a Graphing Utility to Graph Parametric Equations
Answers Credits Index

Algebra and Trigonometry

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A Hardback by Michael Sullivan

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    View other formats and editions of Algebra and Trigonometry by Michael Sullivan

    Publisher: Pearson Education (US)
    Publication Date: 06/02/2019
    ISBN13: 9780135163078, 978-0135163078
    ISBN10: 0135163072
    Also in:
    Mathematics Algebra Calculus and mathematical analysis

    Description

    Book Synopsis


    Table of Contents
    Table of Contents

    1. Review
      • R.1 Real Numbers
      • R.2 Algebra Essentials
      • R.3 Geometry Essentials
      • R.4 Polynomials
      • R.5 Factoring Polynomials
      • R.6 Synthetic Division
      • R.7 Rational Expressions
      • R.8 nth Roots; Rational Exponents
    2. Equations and Inequalities
      • 1.1 Linear Equations
      • 1.2 Quadratic Equations
      • 1.3 Complex Numbers; Quadratic Equations in the Complex Number System
      • 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations
      • 1.5 Solving Inequalities
      • 1.6 Equations and Inequalities Involving Absolute Value
      • 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
      • Chapter 1 Review, Test, and Projects
    3. Graphs
      • 2.1 The Distance and Midpoint Formulas
      • 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry
      • 2.3 Lines
      • 2.4 Circles
      • 2.5 Variation
      • Chapter 2 Review, Test, and Projects
    4. Functions and Their Graphs
      • 3.1 Functions
      • 3.2 The Graph of a Function
      • 3.3 Properties of Functions
      • 3.4 Library of Functions; Piecewise-defined Functions
      • 3.5 Graphing Techniques: Transformations
      • 3.6 Mathematical Models: Building Functions
      • Chapter 3 Review, Test, and Projects
    5. Linear and Quadratic Functions
      • 4.1 Properties of Linear Functions and Linear Models
      • 4.2 Building Linear Models from Data
      • 4.3 Quadratic Functions and Their Properties
      • 4.4 Build Quadratic Models from Verbal Descriptions and from Data
      • 4.5 Inequalities Involving Quadratic Functions
      • Chapter 4 Review, Test, and Projects
    6. Polynomial and Rational Functions
      • 5.1 Polynomial Functions
      • 5.2 Graphing Polynomials Functions; Models
      • 5.3 Properties of Rational Functions
      • 5.4 The Graph of a Rational Function
      • 5.5 Polynomial and Rational Inequalities
      • 5.6 The Real Zeros of a Polynomial Function
      • Chapter 5 Review, Test, and Projects
    7. Exponential and Logarithmic Functions
      • 6.1 Composite Functions
      • 6.2 One-to-One Functions; Inverse Functions
      • 6.3 Exponential Functions
      • 6.4 Logarithmic Functions
      • 6.5 Properties of Logarithms
      • 6.6 Logarithmic and Exponential Equations
      • 6.7 Financial Models
      • 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
      • 6.9 Building Exponential, Logarithmic, and Logistic Models from Data
      • Chapter 6 Review, Test, and Projects
    8. Trigonometric Functions
      • 7.1 Angles, Arc, Length, and Circular Motion
      • 7.2 Right Triangle Trigonometry
      • 7.3 Computing the Values of Trigonometric Functions of Acute Angles
      • 7.4 Trigonometric Functions of Any Angle
      • 7.5 Unit Circle Approach; Properties of the Trigonometric Functions
      • 7.6 Graphs of the Sine and Cosine Functions
      • 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
      • 7.8 Phase Shift; Sinusoidal Curve Fitting
      • Chapter 7 Review, Test, and Projects
    9. Analytic Trigonometry
      • 8.1 The Inverse Sine, Cosine, and Tangent Functions
      • 8.2 The Inverse Trigonometric Functions (Continued)
      • 8.3 Trigonometric Equations
      • 8.4 Trigonometric Identities
      • 8.5 Sum and Difference Formulas
      • 8.6 Double-angle and Half-angle Formulas
      • 8.7 Product-to-Sum and Sum-to-Product Formulas
      • Chapter 8 Review, Test, and Projects
    10. Applications of Trigonometric Functions
      • 9.1 Applications Involving Right Triangles
      • 9.2 The Law of Sines
      • 9.3 The Law of Cosines
      • 9.4 Area of a Triangle
      • 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves
      • Chapter 9 Review, Test, and Projects
    11. Polar Coordinates; Vectors
      • 10.1 Polar Coordinates
      • 10.2 Polar Equations and Graphs
      • 10.3 The Complex Plane; De Moivre’s Theorem
      • 10.4 Vectors
      • 10.5 The Dot Product
      • Chapter 10 Review, Test, and Projects
    12. Analytic Geometry
      • 11.1 Conics
      • 11.2 The Parabola
      • 11.3 The Ellipse
      • 11.4 The Hyperbola
      • 11.5 Rotation of Axes; General Form of a Conic
      • 11.6 Polar Equations of Conics
      • 11.7 Plane Curves and Parametric Equations
      • Chapter 11 Review, Test, and Projects
    13. Systems of Equations and Inequalities
      • 12.1 Systems of Linear Equations: Substitution and Elimination
      • 12.2 Systems of Linear Equations: Matrices
      • 12.3 Systems of Linear Equations: Determinants
      • 12.4 Matrix Algebra
      • 12.5 Partial Fraction Decomposition
      • 12.6 Systems of Nonlinear Equations
      • 12.7 Systems of Inequalities
      • 12.8 Linear Programming
      • Chapter 12 Review, Test, and Projects
    14. Sequences; Induction; the Binomial Theorem
      • 13.1 Sequences
      • 13.2 Arithmetic Sequences
      • 13.3 Geometric Sequences; Geometric Series
      • 13.4 Mathematical Induction
      • 13.5 The Binomial Theorem
      • Chapter 13 Review, Test, and Projects
    15. Counting and Probability
      • 14.1 Counting
      • 14.2 Permutations and Combinations
      • 14.3 Probability
      • Chapter 14 Review, Test, and Projects
    Appendix: Graphing Utilities
    • A.1 The Viewing Rectangle
    • A.2 Using a Graphing Utility to Graph Equations
    • A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry
    • A.4 Using a Graphing Utility to Solve Equations
    • A.5 Square Screens
    • A.6 Using a Graphing Utility to Graph Inequalities
    • A.7 Using a Graphing Utility to Solve Systems of Linear Equations
    • A.8 Using a Graphing Utility to Graph a Polar Equation
    • A.9 Using a Graphing Utility to Graph Parametric Equations
    Answers Credits Index

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