Algebra and Trigonometry, 5th Edition

Algebra and Trigonometry, 5th Edition

by Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
Released January 2015
Publisher(s): Pearson
ISBN: 9780136747512

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Book description

For courses in algebra and trigonometry.

Visualize. Interact. Succeed.

Beecher, Penna, and Bittinger’s Algebra and Trigonometry is known for enabling students to “see the math” through its focus on visualization and early introduction to functions. With the Fifth Edition, the authors continue to innovate by creating and positioning review material to provide a more effective tool for teachers and students.

25 Just-In-Time review topics are placed throughout the text and MyMathLab to help students right when they need it most.

This, along with the existing Mid-chapter Mixed Review exercises, Study Guide summaries, and the new MyMathLab with Integrated Review course, students have an unparalleled amount of review resources to help them be successful in the course.

Also available with MyMathLab™

MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. With this edition, the authors focused on developing MyMathLab features that help better prepare students and get them thinking more visually and conceptually.

Table of contents

  1. Algebra & Trigonometry
  2. Contents
  3. Preface
    1. Content Changes to the Fifth Edition
    2. Emphasis on Functions
    3. Visual Emphasis
    4. Making Connections
    5. Ongoing Review
  4. Get the most out of MyMathLab®
  5. Resources for Success
  6. To the Student
  7. Chapter 1 Graphs, Functions, and Models
    1. 1.1 Introduction to Graphing
      1. Graphs
        1. Example 1
          1. Solution
      2. Solutions of Equations
        1. Example 2
          1. Solution
      3. Graphs of Equations
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
        3. Example 5
          1. Solution
      4. The Distance Formula
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
      5. Midpoints of Segments
        1. Example 8
          1. Solution
        2. Example 9
          1. Solution
      6. Circles
        1. Example 10
          1. Solution
        2. Example 11
          1. Solution
        3. Visualizing the Graph
        4. 1.1 Exercise Set
          1. Synthesis
    2. 1.2 Functions and Graphs
      1. Functions
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. Notation for Functions
        1. Example 4
          1. Solution
      3. Graphs of Functions
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
      4. Finding Domains of Functions
        1. Example 8
          1. Solution
        2. Example 9
          1. Solution
      5. Visualizing Domain and Range
        1. Example 10
          1. Solution
      6. Applications of Functions
        1. Example 11
          1. Solution
        2. 1.2 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    3. 1.3 Linear Functions, Slope, and Applications
      1. Linear Functions
      2. The Linear Function f(x)=mx+b and Slope
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      3. Applications of Slope
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
        3. Example 5
          1. Solution
      4. Slope–Intercept Equations of Lines
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
      5. Graphing f(x)=mx+b Using m and b
        1. Example 8
          1. Solution
      6. Applications of Linear Functions
        1. Example 9
          1. Solution
    4. Visualizing the Graph
    5. 1.3 Exercise Set
      1. Skill Maintenance
      2. Synthesis
    6. Mid-Chapter Mixed Review
      1. Collaborative Discussion and Writing
    7. 1.4 Equations of Lines and Modeling
      1. Slope–Intercept Equations of Lines
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Point–Slope Equations of Lines
        1. Example 3
          1. Solution
      3. Parallel Lines
      4. Perpendicular Lines
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
      5. Mathematical Models
      6. Curve Fitting
        1. Example 6
          1. Solution
        2. The Correlation Coefficient
    8. 1.4 Exercise Set
      1. Skill Maintenance
      2. Synthesis
    9. 1.5 Linear Equations, Functions, Zeros, and Applications
      1. Linear Equations
        1. Example 1
          1. Solution
            1. Check:
        2. Example 2
          1. Solution
            1. Check:
      2. Special Cases
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. Applications Using Linear Models
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
        4. Example 8
          1. Solution
        5. Example 9
          1. Solution
        6. Example 10
          1. Solution
      4. Zeros of Linear Functions
        1. Example 11
        2. The Intersect Method
        3. The Zero Method
    10. 1.5 Exercise Set
      1. Skill Maintenance
      2. Synthesis
    11. 1.6 Solving Linear Inequalities
      1. Linear Inequalities
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Compound Inequalities
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. An Application
        1. Example 5
          1. Solution
    12. 1.6 Exercise Set
      1. Skill Maintenance
        1. Vocabulary Reinforcement
      2. Synthesis
    13. Chapter 1 Summary and Review
      1. Study Guide
      2. Review Exercises
        1. Synthesis
        2. Collaborative Discussion and Writing
      3. 1 Chapter Test
        1. Synthesis
  8. Chapter 2 More on Functions
    1. 2.1 Increasing, Decreasing, and Piecewise Functions; Applications
      1. Increasing, Decreasing, and Constant Functions
        1. Example 1
          1. Solution
      2. Relative Maximum and Minimum Values
        1. Example 2
          1. Solution
      3. Applications of Functions
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      4. Functions Defined Piecewise
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
        4. Example 8
          1. Solution
        5. Example 9
          1. Solution
        6. 2.1 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    2. 2.2 The Algebra of Functions
      1. The Algebra of Functions: Sums, Differences, Products, and Quotients
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Difference Quotients
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
        3. Example 5
          1. Solution
        4. 2.2 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    3. 2.3 The Composition of Functions
      1. The Composition of Functions
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. Decomposing a Function as a Composition
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
        3. 2.3 Exercise Set
          1. Skill Maintenance
          2. Synthesis
        4. Mid-Chapter Mixed Review
          1. Collaborative Discussion and Writing
    4. 2.4 Symmetry
      1. Symmetry
        1. Example 1
        2. Example 2
      2. Even Functions and Odd Functions
        1. Example 3
    5. 2.4 Exercise Set
      1. Skill Maintenance
      2. Synthesis
    6. 2.5 Transformations
      1. Transformations of Functions
      2. Vertical Translations and Horizontal Translations
        1. Example 1
          1. Solution
      3. Reflections
        1. Example 2
          1. Solution
      4. Vertical and Horizontal Stretchings and Shrinkings
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
        3. Visualizing the Graph
      5. 2.5 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    7. 2.6 Variation and Applications
      1. Direct Variation
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Inverse Variation
        1. Example 3
          1. Solution
        2. Example 4 Filling a Swimming Pool.
          1. Solution
      3. Combined Variation
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
        4. Example 8
          1. Solution
      4. 2.6 Exercise Set
        1. Skill Maintenance
          1. Vocabulary Reinforcement
          2. Synthesis
    8. Chapter 2 Summary and Review
      1. Study Guide
      2. Review Exercises
        1. Synthesis
        2. Collaborative Discussion and Writing
      3. 2 Chapter Test
        1. Synthesis
  9. Chapter 3 Quadratic Functions and Equations; Inequalities
    1. 3.1 The Complex Numbers
      1. The Complex-Number System
        1. Example 1
          1. Solution
      2. Addition and Subtraction
        1. Example 2
          1. Solution
      3. Multiplication
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      4. Conjugates and Division
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
      5. 3.1 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    2. 3.2 Quadratic Equations, Functions, Zeros, and Models
      1. Quadratic Equations and Quadratic Functions
        1. Quadratic Equations
        2. Quadratic Functions
        3. Example 1
        4. Example 2
      2. Completing the Square
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. Using the Quadratic Formula
        1. Example 5
          1. Solution
        2. Example 6
      4. The Discriminant
      5. Equations Reducible to Quadratic
        1. Example 7
        2. Example 8
          1. Solution
      6. Applications
        1. Example 9
          1. Solution
        2. Example 10
          1. Solution
        3. Example 11
          1. Solution
      7. 3.2 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    3. 3.3 Analyzing Graphs of Quadratic Functions
      1. Graphing Quadratic Functions of the Type f(x)=a(x−h)2+k
      2. Graphing Quadratic Functions of the Type f(x)=ax2+bx+c, a≠0
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
      3. Applications
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
      4. Visualizing the Graph
      5. 3.3 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    4. Mid-Chapter Mixed Review
      1. Collaborative Discussion and Writing
    5. 3.4 Solving Rational Equations and Radical Equations
      1. Rational Equations
        1. Example 1
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. Radical Equations
        1. Example 4
          1. Solution
        2. Example 5
        3. Example 6
          1. Solution
      3. 3.4 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    6. 3.5 Solving Equations and Inequalities with Absolute Value
      1. Equations with Absolute Value
        1. Example 1
        2. Example 2
          1. Solution
      2. Inequalities with Absolute Value
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. 3.5 Exercise Set
        1. Skill Maintenance
          1. Vocabulary Reinforcement
        2. Synthesis
    7. Chapter 3 Summary and Review
      1. Study Guide
      2. Review Exercises
        1. Synthesis
        2. Collaborative Discussion and Writing
    8. 3 Chapter Test
      1. Synthesis
  10. Chapter 4 Polynomial Functions and Rational Functions
    1. 4.1 Polynomial Functions and Models
      1. The Leading-Term Test
        1. Example 1
          1. Solution
      2. Finding Zeros of Polynomial Functions
        1. Example 2
          1. Solution
        2. Example 3
          1. Solution
        3. Example 4
          1. Solution
        4. Example 5
          1. Solution
        5. Example 6
          1. Solution
      3. Polynomial Models
        1. Example 7
          1. Solution
        2. 4.1 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    2. 4.2 Graphing Polynomial Functions
      1. Graphing Polynomial Functions
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. The Intermediate Value Theorem
        1. Example 4
          1. Solution
        2. Visualizing the Graph
        3. 4.2 Exercise Set
          1. Skill Maintenance
    3. 4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
      1. Division and Factors
        1. Example 1
          1. Solution
      2. The Remainder Theorem and Synthetic Division
        1. Example 2
          1. Solution
        2. Example 3
          1. Solution
        3. Example 4
          1. Solution
        4. Example 5
          1. Solution
      3. Finding Factors of Polynomials
        1. Example 6
          1. Solution
        2. 4.3 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    4. Mid-Chapter Mixed Review
      1. Collaborative Discussion and Writing
    5. 4.4 Theorems about Zeros of Polynomial Functions
      1. The Fundamental Theorem of Algebra
      2. Finding Polynomials with Given Zeros
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      3. Zeros of Polynomial Functions with Real Coefficients
      4. Rational Coefficients
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      5. Integer Coefficients and the Rational Zeros Theorem
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
      6. Descartes’ Rule of Signs
        1. Example 7
          1. Solution
        2. Example 8
          1. Solution
        3. Example 9
          1. Solution
        4. Example 10
          1. Solution
        5. 4.4 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    6. 4.5 Rational Functions
      1. The Domain of a Rational Function
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Asymptotes
        1. Vertical Asymptotes
          1. Example 3
            1. Solution
      3. Horizontal Asymptotes
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
        3. Example 6
          1. Solution
        4. Oblique Asymptotes
          1. Example 7
            1. Solution
          2. Example 8
            1. Solution
          3. Example 9
            1. Solution
          4. Example 10
            1. Solution
          5. Example 11
            1. Solution
      4. Applications
        1. Example 12
          1. Solution
        2. Visualizing the Graph
        3. 4.5 Exercise Set
          1. Skill Maintenance
            1. Vocabulary Reinforcement
          2. Synthesis
    7. 4.6 Polynomial Inequalities and Rational Inequalities
      1. Polynomial Inequalities
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
      2. Rational Inequalities
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
        4. 4.6 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    8. Chapter 4 Summary and Review
      1. Study Guide
    9. Review Exercises
      1. Synthesis
      2. Collaborative Discussion and Writing
    10. Chapter Test
      1. Synthesis
  11. Chapter 5 Exponential Functions and Logarithmic Functions
    1. 5.1 Inverse Functions
      1. Inverses
      2. Example 1
        1. Solution
      3. Example 2
        1. Solution
    2. Inverses and One-to-One Functions
      1. Example 3
        1. Solution
      2. Example 4
        1. Solution
      3. Example 5
        1. Solution
    3. Finding Formulas for Inverses
      1. Example 6
        1. Solution
      2. Example 7
        1. Solution
      3. Example 8
        1. Solution
    4. Inverse Functions and Composition
      1. Example 9
        1. Solution
    5. Restricting a Domain
      1. 5.1 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    6. 5.2 Exponential Functions and Graphs
    7. Graphing Exponential Functions
      1. Example 1
        1. Solution
      2. Example 2
        1. Solution
      3. Example 3
        1. Solution
    8. Applications
      1. Example 4
        1. Solution
    9. The Number e
      1. Example 5
        1. Solution
    10. Graphs of Exponential Functions, Base e
      1. Example 6
        1. Solution
      2. Example 7
        1. Solution
      3. 5.2 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    11. 5.3 Logarithmic Functions and Graphs
      1. Logarithmic Functions
        1. Example 1
          1. Solution
        2. Finding Certain Logarithms
          1. Example 2
            1. Solution
        3. Converting Between Exponential Equations and Logarithmic Equations
          1. Example 3
            1. Solution
          2. Example 4
            1. Solution
        4. Finding Logarithms on a Calculator
          1. Example 5
            1. Solution
        5. Natural Logarithms
          1. Example 6
            1. Solution
        6. Changing Logarithmic Bases
          1. Example 7
            1. Solution
          2. Example 8
            1. Solution
        7. Graphs of Logarithmic Functions
          1. Example 9
            1. Solution
          2. Example 10
            1. Solution
          3. Example 11
            1. Solution
        8. Applications
          1. Example 12
            1. Solution
          2. Example 13
            1. Solution
          3. Visualizing the Graph
          4. 5.3 Exercise Set
            1. Skill Maintenance
            2. Synthesis
    12. Mid-Chapter Mixed Review
      1. Collaborative Discussion and Writing
    13. 5.4 Properties of Logarithmic Functions
      1. Logarithms of Products
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Logarithms of Powers
        1. Example 3
          1. Solution
      3. Logarithms of Quotients
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
      4. Applying the Properties
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
        3. Example 8
          1. Solution
        4. Example 9
          1. Solution
      5. Simplifying Expressions of the Type loga ax and aloga x
        1. Example 10
          1. Solution
        2. Example 11
          1. Solution
        3. 5.4 Exercise Set
    14. 5.5 Solving Exponential Equations and Logarithmic Equations
      1. Solving Exponential Equations
        1. Example 1
        2. Example 2
        3. Example 3
        4. Example 4
        5. Example 5
      2. Solving Logarithmic Equations
        1. Example 6
        2. Example 7
        3. Example 8
        4. Example 9
        5. 5.5 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    15. 5.6 Applications and Models: Growth and Decay; Compound Interest
      1. Population Growth
        1. Example 1
          1. Solution
      2. Interest Compounded Continuously
        1. Example 2
          1. Solution
        2. Example 3
          1. Solution
      3. Models of Limited Growth
        1. Example 4
          1. Solution
      4. Exponential Decay
        1. Example 5
          1. Solution
      5. 5.6 Exercise Set
        1. Skill Maintenance
          1. Vocabulary Reinforcement
        2. Synthesis
    16. Chapter 5 Summary and Review
      1. Study Guide
      2. Review Exercises
        1. Synthesis
        2. Collaborative Discussion and Writing
    17. Chapter Test
      1. Synthesis
  12. Chapter 6 The Trigonometric Functions
    1. 6.1 Trigonometric Functions of Acute Angles
      1. The Trigonometric Ratios
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. The Six Functions Related
        1. Example 4
          1. Solution
      3. Function Values of 30°, 45° , and 60°
        1. Example 5 Height of a Fireworks Display.
          1. Solution
      4. Function Values of Any Acute Angle
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
        3. Example 8
          1. Solution
        4. Example 9
          1. Solution
        5. Example 10 Ladder Safety.
          1. Solution
      5. Cofunctions and Complements
        1. Example 11
          1. Solution
        2. 6.1 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    2. 6.2 Applications of Right Triangles
      1. Solving Right Triangles
        1. Example 1
          1. Solution
        2. Example 2
        3. Solution
    3. Applications
      1. Example 3 Walking at Niagara Falls.
        1. Solution
      2. Example 4 Rafters for a House.
        1. Solution
      3. Example 5 Gondola Aerial Lift.
        1. Solution
      4. Example 6 Height of a Bamboo Plant.
        1. Solution
    4. Bearing: First-Type
      1. Example 7 Distance to a Forest Fire.
        1. Solution
      2. Example 8 U.S. Cellular Field.
        1. Solution
        2. 6.2 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    5. 6.3 Trigonometric Functions of Any Angle
      1. Angles, Rotations, and Degree Measure
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2.   Trigonometric Functions of Angles or Rotations
        1. Example 3
          1. Solution
      3. The Six Functions Related
        1. Example 4
          1. Solution
      4. Terminal Side on an Axis
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
      5. Reference Angles: 30°, 45° and 60°
        1. Example 7
          1. Solution
      6. Function Values for Any Angle
        1. Example 8
          1. Solution
        2. Example 9
          1. Solution
        3. Bearing: Second-Type
          1. Example 10 Aerial Navigation.
            1. Solution
          2. 6.3 Exercise Set
          3. Skill Maintenance
          4. Synthesis
    6. Mid-Chapter Mixed Review
      1. Collaborative Discussion and Writing
    7. 6.4 Radians, Arc Length, and Angular Speed
      1. Distances on the Unit Circle
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Radian Measure
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
        3. Example 5
          1. Solution
        4. Example 6
          1. Solution
      3. Arc Length and Central Angles
        1. Example 7
          1. Solution
        2. Example 8
          1. Solution
      4. Linear Speed and Angular Speed
        1. Example 9 Linear Speed of an Earth Satellite.
          1. Solution
        2. Example 10 Angular Speed of a Capstan.
          1. Solution
        3. Example 11 Angle of Revolution.
          1. Solution
        4. Example 12 Angular Speed of a Gear Wheel.
          1. Solution
        5. 6.4 Exercise Set
          1. Skill Maintenance
            1. Vocabulary Reinforcement
          2. Synthesis
    8. 6.5 Circular Functions: Graphs and Properties
      1. Reflections on the Unit Circle
        1. Example 1
          1. Solution
      2. Finding Function Values
        1. Example 2
          1. Solution
        2. Example 3
          1. Solution
    9. Graphs of the Sine and Cosine Functions
    10. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
      1. 6.5 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    11. 6.6 Graphs of Transformed Sine and Cosine Functions
      1. Variations of Basic Graphs
        1. The Constant D
          1. Example 1
            1. Solution
        2. The Constant A
          1. Example 2
        3. Solution
          1. Example 3
          2. Solution
        4. The Constant B
          1. Example 4
            1. Solution
        5. The Constant C
          1. Example 5
            1. Solution
          2. Example 6
            1. Solution
          3. Example 7
            1. Solution
          4. Example 8
            1. Solution
      2. Graphs of Sums: Addition of Ordinates
        1. Example 9
          1. Solution
      3. Damped Oscillation: Multiplication of Ordinates
        1. Example 10
          1. Solution
        2. Visualizing the Graph
        3. 6.6 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    12. Chapter 6 Summary and Review
      1. Study Guide
        1. Review Exercises
          1. Synthesis
          2. Collaborative Discussion and Writing
          3. 6 Chapter Test
            1. Synthesis
  13. Chapter 7 Trigonometric Identities, Inverse Functions, and Equations
    1. 7.1 Identities: Pythagorean and Sum and Difference
      1. Pythagorean Identities
      2. Simplifying Trigonometric Expressions
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
        5. Example 5
          1. Solution
        6. Example 6
          1. Solution
        7. Example 7
          1. Solution
      3. Sum and Difference Identities
        1. Example 8
          1. Solution
        2. Example 9
          1. Solution
        3. Example 10
          1. Solution
        4. Example 11
          1. Solution
        5. Example 12
          1. Solution
        6. 7.1 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    2. 7.2 Identities: Cofunction, Double-Angle, and Half-Angle
      1. Cofunction Identities
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Double-Angle Identities
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. Half-Angle Identities
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. 7.2 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    3. 7.3 Proving Trigonometric Identities
      1. The Logic of Proving Identities
      2. Proving Identities
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
        5. Example 5
          1. Solution
      3. Product-to-Sum and Sum-to-Product Identities
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
        3. 7.3 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    4. Mid-Chapter Mixed Review
      1. Collaborative Discussion and Writing
    5. 7.4 Inverses of the Trigonometric Functions
      1.  Restricting Ranges to Define Inverse Functions
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2.  Composition of Trigonometric Functions and Their Inverses
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
        3. Example 5
          1. Solution
        4. Example 6
          1. Solution
        5. Example 7
          1. Solution
        6. 7.4 Exercise Set
          1. Skill Maintenance
            1. Vocabulary Reinforcement
          2. Synthesis
    6. 7.5 Solving Trigonometric Equations
      1. Example 1
      2. Example 2
      3. Example 3
        1. Solution
      4. Example 4
        1. Solution
      5. Example 5
      6. Example 6
      7. Example 7
        1. Solution
      8. Example 8
        1. Solution
      9. Example 9
        1. Solution
      10. Example 10
      11. Example 11
        1. Solution
      12. Visualizing the Graph
      13. 7.5 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    7. Chapter 7 Summary and Review
      1. Study Guide
    8. Review Exercises
      1. Synthesis
      2. Collaborative Discussion and Writing
    9. 7 Chapter Test
      1. Synthesis
  14. Chapter 8 Applications of Trigonometry
    1. 8.1 The Law of Sines
      1. Solving Oblique Triangles
      2. The Law of Sines
      3. Solving Triangles (AAS and ASA)
        1. Example 1
          1. Solution
        2. Example 2 Vietnam Veterans Memorial.
          1. Solution
      4. Solving Triangles (SSA)
        1. Angle B Is Acute
          1. Case 1: No solution
          2. Case 2: One solution
          3. Case 3: Two solutions
          4. Case 4: One solution
          5. Case 5: One solution
        2. Angle B Is Obtuse
          1. Case 6: No solution
          2. Case 7: No solution
          3. Case 8: One solution
        3. Example 3 No solution.
          1. Solution
        4. Example 4 One solution.
          1. Solution
        5. Example 5 Two solutions.
          1. Solution
      5. The Area of a Triangle
        1. Example 6 Area of a Triangular Garden.
          1. Solution
        2. 8.1 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    2. 8.2 The Law of Cosines
      1. The Law of Cosines
      2. Solving Triangles (SAS)
        1. Example 1
          1. Solution
        2. Example 2 Recording Studio.
          1. Solution
      3. Solving Triangles (SSS)
        1. Example 3
          1. Solution
        2. Example 4 Wedge Bevel.
          1. Solution
        3. Example 5
          1. Solution
        4. 8.2 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    3. 8.3 Complex Numbers: Trigonometric Notation
      1. Graphical Representation
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Trigonometric Notation for Complex Numbers
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. Multiplication and Division with Trigonometric Notation
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
        4. Example 8
          1. Solution
      4. Powers of Complex Numbers
        1. Example 9
          1. Solution
      5. Roots of Complex Numbers
        1. Example 10
          1. Solution
        2. Example 11
          1. Solution
        3. Example 12
          1. Solution
      6. 8.3 Exercise Set
        1. Skill Maintenance
        2. Synthesis
      7. Mid-Chapter Mixed Review
        1. Collaborative Discussion and Writing
    4. 8.4 Polar Coordinates and Graphs
      1. Polar Coordinates
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. Polar Equations and Rectangular Equations
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
      3. Graphing Polar Equations
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
        3. Visualizing the Graph
        4. 8.4 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    5. 8.5 Vectors and Applications
    6. 8.6 Vector Operations
    7. Chapter 8 Summary and Review Study Guide
    8. Review Exercises
      1. Synthesis
      2. Collaborative Discussion and Writing
    9. Chapter Test
      1. Synthesis
  15. Chapter 9 Systems of Equations and Matrices
    1. 9.1 Systems of Equations in Two Variables
      1. Solving Systems of Equations Graphically
        1. Example 1
          1. Solution
      2. The Substitution Method
        1. Example 2
          1. Solution
      3. The Elimination Method
        1. Example 3
        2. Example 4
        3. Example 5
          1. Solution
      4. Applications
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
        3. Example 8
          1. Solution
      5. Visualizing the Graph
      6. 9.1 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    2. 9.2 Systems of Equations in Three Variables
      1. Solving Systems of Equations in Three Variables
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Applications
        1. Example 3
          1. Solution
      3. Mathematical Models and Applications
        1. Example 4
          1. Solution
      4. 9.2 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    3. 9.3 Matrices and Systems of Equations
      1. Matrices and Row-Equivalent Operations
      2. Gaussian Elimination with Matrices
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      3. Gauss–Jordan Elimination
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      4. 9.3 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    4. 9.4 Matrix Operations
      1. Matrix Addition and Subtraction
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. Scalar Multiplication
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
      3. Products of Matrices
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
      4. Matrix Equations
        1. Example 8
          1. Solution
      5. 9.4 Exercise Set
        1. Skill Maintenance
        2. Synthesis
      6. Mid-Chapter Mixed Review
        1. Collaborative Discussion and Writing
    5. 9.5 Inverses of Matrices
      1. The Identity Matrix
        1. Example 1
          1. Solution
      2. The Inverse of a Matrix
        1. Example 2
          1. Solution
        2. Example 3
          1. Solution
        3. Example 4
          1. Solution
      3. Solving Systems of Equations
        1. Example 5
          1. Solution
      4. 9.5 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    6. 9.6 Determinants and Cramer’s Rule
      1. Determinants of Square Matrices
        1. Example 1
          1. Solution
      2. Evaluating Determinants Using Cofactors
        1. Example 2
          1. Solution
        2. Example 3
          1. Solution
        3. Example 4
          1. Solution
      3. Cramer’s Rule
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
      4. 9.6 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    7. 9.7 Systems of Inequalities and Linear Programming
      1. Graphs of Linear Inequalities
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
      2. Systems of Linear Inequalities
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
      3. Applications: Linear Programming
        1. Example 7
          1. Solution
      4. 9.7 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    8. 9.8 Partial Fractions
      1. Partial Fraction Decompositions
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
        5. Example 5
          1. Solution
      2. 9.8 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    9. Chapter 6 Summary and Review
      1. Study Guide
      2. Review Exercises
        1. Synthesis
        2. Collaborative Discussion and Writing
      3. 6 Chapter Test
        1. Synthesis
  16. Chapter 10 Analytic Geometry Topics
    1. 10.1 The Parabola
      1. Parabolas
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Finding Standard Form by Completing the Square
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. Applications
      4. 10.1 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    2. 10.2 The Circle and the Ellipse
      1. Circles
        1. Example 1
          1. Solution
      2. Ellipses
        1. Example 2
          1. Solution
        2. Example 3
          1. Solution
        3. Example 4
          1. Solution
      3. Applications
      4. 10.2 Exercise Set
        1. Skill Maintenance
          1. Vocabulary Reinforcement
        2. Synthesis
    3. 10.3 The Hyperbola
      1. Standard Equations of Hyperbolas
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. Applications
      3. 10.3 Exercise Set
        1. Skill Maintenance
        2. Synthesis
    4. 10.4 Nonlinear Systems of Equations and Inequalities
      1. Nonlinear Systems of Equations
        1. Example 1
        2. Example 2
        3. Example 3
        4. Example 4
      2. Modeling and Problem Solving
        1. Example 5
          1. Solution
      3. Nonlinear Systems of Inequalities
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
      4. Visualizing the Graph
      5. 10.4 Exercise Set
        1. Skill Maintenance
        2. Synthesis
          1. Mid-Chapter Mixed Review
            1. Collaborative Discussion and Writing
      6. 10.5 Rotation of Axes
        1. Rotation of Axes
          1. Example 1
            1. Solution
          2. Example 2
            1. Solution
        2. The Discriminant
          1. Example 3
            1. Solution
          2. Example 4
            1. Solution
        3. 10.5 Exercise Set
          1. Skill Maintenance
          2. Synthesis
      7. 10.6 Polar Equations of Conics
        1. Polar Equations of Conics
          1. Example 1
            1. Solution
          2. Example 2
            1. Solution
          3. Example 3
            1. Solution
        2. Converting from Polar Equations to Rectangular Equations
          1. Example 4
            1. Solution
        3. Finding Polar Equations of Conics
          1. Example 5
            1. Solution
          2. 10.6 Exercise Set
            1. Skill Maintenance
            2. Synthesis
      8. 10.7 Parametric Equations
        1. Graphing Parametric Equations
          1. Example 1
            1. Solution
        2. Determining a Rectangular Equation for Given Parametric Equations
          1. Example 2
            1. Solution
          2. Example 3
            1. Solution
        3. Determining Parametric Equations for a Given Rectangular Equation
          1. Example 4
            1. Solution
        4. Applications
          1. Example 5 Projectile Motion.
            1. Solution
        5. Exercise Set 10.7
          1. Skill Maintenance
          2. Synthesis
    5. Chapter 10 Summary and Review Study Guide
    6. Review Exercises
      1. Synthesis
      2. Collaborative Discussion and Writing
      3. Chapter Test
      4. Synthesis
  17. Chapter 11 Sequences, Series, and Combinatorics
    1. 11.1 Sequences and Series
      1. Sequences
        1. Example 1
          1. Solution
      2. Finding the General Term
        1. Example 2
          1. Solution
      3. Sums and Series
        1. Example 3
          1. Solution
      4. Sigma Notation
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
      5. Recursive Definitions
        1. Example 6
          1. Solution
        2. 11.1 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    2. 11.2 Arithmetic Sequences and Series
      1. Arithmetic Sequences
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
      2. Sum of the First n Terms of an Arithmetic Sequence
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
        3. Example 7
          1. Solution
      3. Applications
        1. Example 8
          1. Solution
        2. Example 9
          1. Solution
        3. 11.2 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    3. 11.3 Geometric Sequences and Series
      1. Geometric Sequences
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
      2. Sum of the First n Terms of a Geometric Sequence
        1. Example 4
          1. Solution
        2. Example 5
          1. Solution
      3. Infinite Geometric Series
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
      4. Applications
        1. Example 8
          1. Solution
        2. Example 9
          1. Solution
        3. Example 10
          1. Solution
        4. Visualizing the Graph
        5. 11.3 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    4. 11.4 Mathematical Induction
      1. Proving Infinite Sequences of Statements
        1. Example 1
        2. Example 2
        3. Example 3
        4. 11.4 Exercise Set
          1. Skill Maintenance
          2. Synthesis
        5. Mid-Chapter Mixed Review
          1. Collaborative Discussion and Writing
    5. 11.5 Combinatorics: Permutations
      1. Permutations
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
      2. Factorial Notation
        1. Example 5
          1. Solution
      3. Permutations of n Objects Taken k at a Time
        1. Example 6
          1. Solution
        2. Example 7
          1. Solution
        3. Example 8
          1. Solution
        4. Example 9
          1. Solution
      4. Permutations of Sets with Nondistinguishable Objects
        1. Example 10
          1. Solution
        2. 11.5 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    6. 11.6 Combinatorics: Combinations
      1. Combinations
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
        3. Example 3
          1. Solution
        4. Example 4
          1. Solution
        5. Example 5
          1. Solution
        6. 11.6 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    7. 11.7 The Binomial Theorem
      1. Binomial Expansion Using Pascal’s Triangle
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      2. Binomial Expansion Using Factorial Notation
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
      3. Finding a Specific Term
        1. Example 5
          1. Solution
        2. Example 6
          1. Solution
      4. Total Number of Subsets
        1. Example 7
          1. Solution
        2. Example 8
          1. Solution
        3. 11.7 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    8. 11.8 Probability
      1. Experimental Probability and Theoretical Probability
      2. Computing Experimental Probabilities
        1. Example 1
          1. Solution
        2. Example 2
          1. Solution
      3. Theoretical Probability
        1. Example 3
          1. Solution
        2. Example 4
          1. Solution
        3. Example 5
          1. Solution
        4. Example 6
          1. Solution
        5. Example 7
          1. Solution
        6. Example 8
          1. Solution
        7. Example 9
          1. Solution
        8. Example 10
          1. Solution
        9. 11.8 Exercise Set
          1. Skill Maintenance
          2. Synthesis
    9. Chapter 11 Summary and Review
      1. Study Guide
      2. Review Exercises
        1. Synthesis
        2. Collaborative Discussion and Writing
      3. 11 Chapter Test
        1. Synthesis
  18. Just-In-Time Review
    1. Real Numbers
    2. Properties of Real Numbers
    3. Absolute Value
    4. Operations with Real Numbers
    5. Order on the Number Line
    6. Interval Notation
    7. Integers as Exponents
    8. Scientific Notation
    9. Order of Operations
    10. Introduction to Polynomials
    11. Add and Subtract Polynomials
    12. Multiply Polynomials
    13. Factor Polynomials
    14. Equation-Solving Principles
    15. Inequality-Solving Principles
    16. Principle of Zero Products
    17. Principle of Square Roots
    18. Simplify Rational Expressions
    19. Multiply and Divide Rational Expressions
    20. Add and Subtract Rational Expressions
    21. Simplify Complex Rational Expressions
    22. Simplify Radical Expressions
    23. Rationalizing Denominators
    24. Rational Exponents
    25. Pythagorean Theorem
  19. Answers
    1. Visualizing the Graph
    2. Exercise Set 1.1
    3. Exercise Set 1.2
    4. Visualizing the Graph
    5. Exercise Set 1.3
    6. Mid-Chapter Mixed Review: Chapter 1
    7. Exercise Set 1.4
    8. Exercise Set 1.5
    9. Exercise Set 1.6
    10. Review Exercises: Chapter 1
    11. Test: Chapter 1
    12. Exercise Set 2.1
    13. Exercise Set 2.2
    14. Exercise Set 2.3
    15. Mid-Chapter Mixed Review: Chapter 2
    16. Exercise Set 2.4
    17. Visualizing the Graph
    18. Exercise Set 2.5
    19. Exercise Set 2.6
    20. Review Exercises: Chapter 2
    21. Test: Chapter 2
    22. Exercise Set 3.1
    23. Exercise Set 3.2
    24. Visualizing the Graph
    25. Exercise Set 3.3
    26. Mid-Chapter Mixed Review: Chapter 3
    27. Exercise Set 3.4
    28. Exercise Set 3.5
    29. Review Exercises: Chapter 3
    30. Test: Chapter 3
    31. Exercise Set 4.1
    32. Visualizing the Graph
    33. Exercise Set 4.2
    34. Exercise Set 4.3
    35. Mid-Chapter Mixed Review: Chapter 4
    36. Exercise Set 4.4
    37. Visualizing the Graph
    38. Exercise Set 4.5
    39. Exercise Set 4.6
    40. Review Exercises: Chapter 4
    41. Test: Chapter 4
    42. Exercise Set 5.1
    43. Exercise Set 5.2
    44. Visualizing the Graph
    45. Exercise Set 5.3
    46. Mid-Chapter Mixed Review: Chapter 5
    47. Exercise Set 5.4
    48. Exercise Set 5.5
    49. Exercise Set 5.6
    50. Review Exercises: Chapter 5
    51. Test: Chapter 5
    52. Exercise Set 6.1
    53. Exercise Set 6.2
    54. Exercise Set 6.3
    55. Mid-Chapter Mixed Review: Chapter 6
    56. Exercise Set 6.4
    57. Exercise Set 6.5
    58. Visualizing the Graph
    59. Exercise Set 6.6
    60. ReviewExercises: Chapter 6
    61. Test: Chapter 6
    62. Exercise Set 7.1
    63. Exercise Set 7.2
    64. Exercise Set 7.3
    65. Mid-Chapter Mixed Review: Chapter 7
    66. Exercise Set 7.4
    67. Visualizing the Graph
    68. Exercise Set 7.5
    69. Review Exercises: Chapter 7
    70. Test: Chapter 7
    71. Exercise Set 8.1
    72. Exercise Set 8.2
    73. Exercise Set 8.3
    74. Mid-Chapter Mixed Review: Chapter 8
    75. Visualizing the Graph
    76. Exercise Set 8.4
    77. Exercise Set 8.5
    78. Exercise Set 8.6
    79. Review Exercises: Chapter 8
    80. Test: Chapter 8
    81. Visualizing the Graph
    82. Exercise Set 9.1
    83. Exercise Set 9.2
    84. Exercise Set 9.3
    85. Exercise Set 9.4
    86. Mid-Chapter Mixed Review: Chapter 9
    87. Exercise Set 9.5
    88. Exercise Set 9.6
    89. Exercise Set 9.7
    90. Exercise Set 9.8
    91. Review Exercises: Chapter 9
    92. Test: Chapter 9
    93. Exercise Set 10.1
    94. Exercise Set 10.2
    95. Exercise Set 10.3
    96. Visualizing the Graph
    97. Exercise Set 10.4
    98. Mid-Chapter Mixed Review: Chapter 10
    99. Exercise Set 10.5
    100. Exercise Set 10.6
    101. Exercise Set 10.7
    102. Review Exercises: Chapter 10
    103. Test: Chapter 10
    104. Exercise Set 11.1
    105. Exercise Set 11.2
    106. Visualizing the Graph
    107. Exercise Set 11.3
    108. Exercise Set 11.4
    109. Mid-Chapter Mixed Review: Chapter 11
    110. Exercise Set 11.5
    111. Exercise Set 11.6
    112. Exercise Set 11.7
    113. Exercise Set 11.8
    114. Review Exercises: Chapter 11
    115. Test: Chapter 11
    116. Just-In-Time
  20. Photo Credits
    1. Chapter 1:
    2. Chapter 2:
    3. Chapter 3:
    4. Chapter 4:
    5. Chapter 5:
    6. Chapter 6:
    7. Chapter 7:
    8. Chapter 8:
    9. Chapter 9:
    10. Chapter 10:
    11. Chapter 11:
  21. Index of Applications
    1. Agriculture
    2. Astronomy
    3. Automotive
    4. Biology/Life Sciences
    5. Business
    6. Chemistry
    7. Construction
    8. Consumer
    9. Economics
    10. Education
    11. Engineering
    12. Environment
    13. Finance
    14. General Interest
    15. Geometry
    16. Government
    17. Health/Medicine
    18. Labor
    19. Physics
    20. Social Sciences
    21. Sports/Entertainment
    22. Statistics/Demographics
    23. Technology
    24. Transportation
  22. Index

Product information

  • Title: Algebra and Trigonometry, 5th Edition
  • Author(s): Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger
  • Release date: January 2015
  • Publisher(s): Pearson
  • ISBN: 9780136747512