Chapter 7 Trigonometric Identities, Inverse Functions, and Equations
by Marvin L. Bittinger, Judith A. Penna, Judith A. Beecher
Algebra and Trigonometry, 5th Edition
- Algebra & Trigonometry
- Contents
- Preface
- Get the most out of MyMathLab®
- Resources for Success
- To the Student
- Chapter 1 Graphs, Functions, and Models
- 1.1 Introduction to Graphing
- 1.2 Functions and Graphs
- 1.3 Linear Functions, Slope, and Applications
- Visualizing the Graph
- 1.3 Exercise Set
- Mid-Chapter Mixed Review
- 1.4 Equations of Lines and Modeling
- 1.4 Exercise Set
- 1.5 Linear Equations, Functions, Zeros, and Applications
- 1.5 Exercise Set
- 1.6 Solving Linear Inequalities
- 1.6 Exercise Set
- Chapter 1 Summary and Review
- Chapter 2 More on Functions
- 2.1 Increasing, Decreasing, and Piecewise Functions; Applications
- 2.2 The Algebra of Functions
- 2.3 The Composition of Functions
- 2.4 Symmetry
- 2.4 Exercise Set
- 2.5 Transformations
- 2.6 Variation and Applications
- Chapter 2 Summary and Review
- Chapter 3 Quadratic Functions and Equations; Inequalities
- 3.1 The Complex Numbers
- 3.2 Quadratic Equations, Functions, Zeros, and Models
- 3.3 Analyzing Graphs of Quadratic Functions
- Mid-Chapter Mixed Review
- 3.4 Solving Rational Equations and Radical Equations
- 3.5 Solving Equations and Inequalities with Absolute Value
- Chapter 3 Summary and Review
- 3 Chapter Test
- Chapter 4 Polynomial Functions and Rational Functions
- 4.1 Polynomial Functions and Models
- 4.2 Graphing Polynomial Functions
- 4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem
- Mid-Chapter Mixed Review
- 4.4 Theorems about Zeros of Polynomial Functions
- 4.5 Rational Functions
- 4.6 Polynomial Inequalities and Rational Inequalities
- Chapter 4 Summary and Review
- Review Exercises
- Chapter Test
- Chapter 5 Exponential Functions and Logarithmic Functions
- 5.1 Inverse Functions
- Inverses and One-to-One Functions
- Finding Formulas for Inverses
- Inverse Functions and Composition
- Restricting a Domain
- 5.2 Exponential Functions and Graphs
- Graphing Exponential Functions
- Applications
- The Number e
- Graphs of Exponential Functions, Base e
- 5.3 Logarithmic Functions and Graphs
- Logarithmic Functions
- Example 1
- Finding Certain Logarithms
- Converting Between Exponential Equations and Logarithmic Equations
- Finding Logarithms on a Calculator
- Natural Logarithms
- Changing Logarithmic Bases
- Graphs of Logarithmic Functions
- Applications
- Example 12
- Example 13
- Visualizing the Graph
- 5.3 Exercise Set
- Skill Maintenance
- Synthesis
- Mid-Chapter Mixed Review
- 5.4 Properties of Logarithmic Functions
- 5.5 Solving Exponential Equations and Logarithmic Equations
- 5.6 Applications and Models: Growth and Decay; Compound Interest
- Chapter 5 Summary and Review
- Chapter Test
- Chapter 6 The Trigonometric Functions
- 6.1 Trigonometric Functions of Acute Angles
- 6.2 Applications of Right Triangles
- Applications
- Bearing: First-Type
- 6.3 Trigonometric Functions of Any Angle
- Mid-Chapter Mixed Review
- 6.4 Radians, Arc Length, and Angular Speed
- 6.5 Circular Functions: Graphs and Properties
- Graphs of the Sine and Cosine Functions
- Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
- 6.6 Graphs of Transformed Sine and Cosine Functions
- Chapter 6 Summary and Review
- Study Guide
- Review Exercises
- Synthesis
- Collaborative Discussion and Writing
- 6 Chapter Test
- Synthesis
- Chapter 7 Trigonometric Identities, Inverse Functions, and Equations
- 7.1 Identities: Pythagorean and Sum and Difference
- 7.2 Identities: Cofunction, Double-Angle, and Half-Angle
- 7.3 Proving Trigonometric Identities
- Mid-Chapter Mixed Review
- 7.4 Inverses of the Trigonometric Functions
- 7.5 Solving Trigonometric Equations
- Chapter 7 Summary and Review
- Review Exercises
- 7 Chapter Test
- Chapter 8 Applications of Trigonometry
- 8.1 The Law of Sines
- 8.2 The Law of Cosines
- 8.3 Complex Numbers: Trigonometric Notation
- 8.4 Polar Coordinates and Graphs
- 8.5 Vectors and Applications
- 8.6 Vector Operations
- Chapter 8 Summary and Review Study Guide
- Review Exercises
- Chapter Test
- Chapter 9 Systems of Equations and Matrices
- 9.1 Systems of Equations in Two Variables
- 9.2 Systems of Equations in Three Variables
- 9.3 Matrices and Systems of Equations
- 9.4 Matrix Operations
- 9.5 Inverses of Matrices
- 9.6 Determinants and Cramer’s RuleDeterminants and Cramer’s Rule
- 9.7 Systems of Inequalities and Linear Programming
- 9.8 Partial Fractions
- Chapter 6 Summary and Review
- Chapter 10 Analytic Geometry Topics
- 10.1 The Parabola
- 10.2 The Circle and the Ellipse
- 10.3 The Hyperbola
- 10.4 Nonlinear Systems of Equations and Inequalities
- Nonlinear Systems of Equations
- Modeling and Problem Solving
- Nonlinear Systems of Inequalities
- Visualizing the Graph
- 10.4 Exercise Set
- 10.5 Rotation of Axes
- 10.6 Polar Equations of Conics
- 10.7 Parametric Equations
- Chapter 10 Summary and Review Study Guide
- Review Exercises
- Chapter 11 Sequences, Series, and Combinatorics
- 11.1 Sequences and Series
- 11.2 Arithmetic Sequences and Series
- 11.3 Geometric Sequences and Series
- 11.4 Mathematical Induction
- 11.5 Combinatorics: Permutations
- 11.6 Combinatorics: Combinations
- 11.7 The Binomial Theorem
- 11.8 Probability
- Chapter 11 Summary and Review
- Just-In-Time Review
- Real Numbers
- Properties of Real Numbers
- Absolute Value
- Operations with Real Numbers
- Order on the Number Line
- Interval Notation
- Integers as Exponents
- Scientific Notation
- Order of Operations
- Introduction to Polynomials
- Add and Subtract Polynomials
- Multiply Polynomials
- Factor Polynomials
- Equation-Solving Principles
- Inequality-Solving Principles
- Principle of Zero Products
- Principle of Square Roots
- Simplify Rational Expressions
- Multiply and Divide Rational Expressions
- Add and Subtract Rational Expressions
- Simplify Complex Rational Expressions
- Simplify Radical Expressions
- Rationalizing Denominators
- Rational Exponents
- Pythagorean Theorem
- Answers
- Visualizing the Graph
- Exercise Set 1.1
- Exercise Set 1.2
- Visualizing the Graph
- Exercise Set 1.3
- Mid-Chapter Mixed Review: Chapter 1
- Exercise Set 1.4
- Exercise Set 1.5
- Exercise Set 1.6
- Review Exercises: Chapter 1
- Test: Chapter 1
- Exercise Set 2.1
- Exercise Set 2.2
- Exercise Set 2.3
- Mid-Chapter Mixed Review: Chapter 2
- Exercise Set 2.4
- Visualizing the Graph
- Exercise Set 2.5
- Exercise Set 2.6
- Review Exercises: Chapter 2
- Test: Chapter 2
- Exercise Set 3.1
- Exercise Set 3.2
- Visualizing the Graph
- Exercise Set 3.3
- Mid-Chapter Mixed Review: Chapter 3
- Exercise Set 3.4
- Exercise Set 3.5
- Review Exercises: Chapter 3
- Test: Chapter 3
- Exercise Set 4.1
- Visualizing the Graph
- Exercise Set 4.2
- Exercise Set 4.3
- Mid-Chapter Mixed Review: Chapter 4
- Exercise Set 4.4
- Visualizing the Graph
- Exercise Set 4.5
- Exercise Set 4.6
- Review Exercises: Chapter 4
- Test: Chapter 4
- Exercise Set 5.1
- Exercise Set 5.2
- Visualizing the Graph
- Exercise Set 5.3
- Mid-Chapter Mixed Review: Chapter 5
- Exercise Set 5.4
- Exercise Set 5.5
- Exercise Set 5.6
- Review Exercises: Chapter 5
- Test: Chapter 5
- Exercise Set 6.1
- Exercise Set 6.2
- Exercise Set 6.3
- Mid-Chapter Mixed Review: Chapter 6
- Exercise Set 6.4
- Exercise Set 6.5
- Visualizing the Graph
- Exercise Set 6.6
- ReviewExercises: Chapter 6
- Test: Chapter 6
- Exercise Set 7.1
- Exercise Set 7.2
- Exercise Set 7.3
- Mid-Chapter Mixed Review: Chapter 7
- Exercise Set 7.4
- Visualizing the Graph
- Exercise Set 7.5
- Review Exercises: Chapter 7
- Test: Chapter 7
- Exercise Set 8.1
- Exercise Set 8.2
- Exercise Set 8.3
- Mid-Chapter Mixed Review: Chapter 8
- Visualizing the Graph
- Exercise Set 8.4
- Exercise Set 8.5
- Exercise Set 8.6
- Review Exercises: Chapter 8
- Test: Chapter 8
- Visualizing the Graph
- Exercise Set 9.1
- Exercise Set 9.2
- Exercise Set 9.3
- Exercise Set 9.4
- Mid-Chapter Mixed Review: Chapter 9
- Exercise Set 9.5
- Exercise Set 9.6
- Exercise Set 9.7
- Exercise Set 9.8
- Review Exercises: Chapter 9
- Test: Chapter 9
- Exercise Set 10.1
- Exercise Set 10.2
- Exercise Set 10.3
- Visualizing the Graph
- Exercise Set 10.4
- Mid-Chapter Mixed Review: Chapter 10
- Exercise Set 10.5
- Exercise Set 10.6
- Exercise Set 10.7
- Review Exercises: Chapter 10
- Test: Chapter 10
- Exercise Set 11.1
- Exercise Set 11.2
- Visualizing the Graph
- Exercise Set 11.3
- Exercise Set 11.4
- Mid-Chapter Mixed Review: Chapter 11
- Exercise Set 11.5
- Exercise Set 11.6
- Exercise Set 11.7
- Exercise Set 11.8
- Review Exercises: Chapter 11
- Test: Chapter 11
- Just-In-Time
- Photo Credits
- Index of Applications
- Agriculture
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- Automotive
- Biology/Life Sciences
- Business
- Chemistry
- Construction
- Consumer
- Economics
- Education
- Engineering
- Environment
- Finance
- General Interest
- Geometry
- Government
- Health/Medicine
- Labor
- Physics
- Social Sciences
- Sports/Entertainment
- Statistics/Demographics
- Technology
- Transportation
- Index
- Review Exercises
- Study Guide
- Logarithmic Functions
Chapter 7 Trigonometric Identities, Inverse Functions, and Equations
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