Cover image for Algebra and Trigonometry, 5th Edition

Algebra and Trigonometry, 5th Edition

Author Marvin L. Bittinger , Judith A. Penna , Judith A. Beecher
Release Date: -0001/11/30
ISBN: 9780136747512
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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
            3. Mid-Chapter Mixed Review
              1. Collaborative Discussion and Writing
            4. 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
            5. 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
            6. 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
            7. Chapter 5 Summary and Review
              1. Study Guide
              2. Review Exercises
                1. Synthesis
                2. Collaborative Discussion and Writing
            8. Chapter Test
              1. Synthesis
          5. 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
                    2. 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
                    3. 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
                    4. 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 RuleDeterminants 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
                    5. 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
                    6. 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
                    7. 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
                    8. 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
                    9. 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:
                    10. 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
                    11. Index
18.222.23.119