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Contents

  1. Introduction

    1. Introduction
    2. About This Book

  2. About the Authors

    1. Authors
  3. Chapter 1: Triangles and Circles

    1. Introduction to Triangles and Circles

      1. Introduction
      2. Class Activities

    2. 1.1 Triangles and Angles

      1. Algebra Refresher
      2. Triangles and Angles
      3. Triangles
      4. Angles
      5. Section 1.1 Summary

    3. 1.2 Similar Triangles

      1. Algebra Refresher
      2. Congruent Triangles
      3. Similar Triangles
      4. Using Proportions with Similar Triangles
      5. Similar Right Triangles
      6. Overlapping Triangles
      7. Section 1.2 Summary

    4. 1.3 Circles

      1. Algebra Refresher
      3. The Distance Formula
      4. Equation for a Circle
      5. Section 1.3 Summary

    5. Chapter 1 Summary and Review

    6. Exercises: 1.1 Triangles and Angles

    7. Exercises: 1.2 Similar Triangles

    8. Exercises: 1.3 Circles

    9. Exercises: Chapter 1 Review Problems

  4. Chapter 2: Trigonometric Ratios

    1. Introduction to the Trigonometric Ratios

      1. Introduction
      2. Class Activities

    2. 2.1 Side and Angle Relationships

      1. Algebra Refresher
      2. Introduction to Triangles
      3. The Triangle Inequality
      4. Right Triangles: The Pythagorean Theorem
      5. Section 2.1 Summary

    3. 2.2 Right Triangle Trigonometry

      1. Algebra Refresher
      2. The Sine of an Angle
      3. Using the Sine Ratio to Find an Unknown Side
      4. The Cosine and the Tangent
      5. The Three Trigonometric Ratios
      6. Section 2.2 Summary

    4. 2.3 Solving Right Triangles

      1. Algebra Refresher
      2. Finding an Angle
      3. The Special Angles
      4. Section 2.3 Summary

    5. Chapter 2 Summary and Review

    6. Exercises: 2.1 Side and Angle Relationships

    7. Exercises: 2.2 Right Triangle Trigonometry

    8. Exercises: 2.3 Solving Right Triangles

    9. Exercises: Chapter 2 Review Problems

  5. Chapter 3: Laws of Sines and Cosines

    1. Introduction to Laws of Sines and Cosines

      1. Introduction
      2. Class Activities

    2. 3.1 Obtuse Angles

      1. Algebra Refresher
      2. Angles in Standard Position
      3. Trigonometric Ratios for Obtuse Angles
      4. Trigonometric Ratios for Supplementary Angles
      5. Supplements of the Special Angles
      6. The Area of a Triangle
      7. Section 3.1 Summary

    3. 3.2 The Law of Sines

      1. Algebra Refresher
      2. Law of Sines
      3. Finding a Side
      4. Solving Triangles with the Law of Sines
      5. Finding an Angle
      6. Applications
      7. Measuring Astronomical Distances
      8. Small Angles: Minutes and Seconds
      9. Section 3.2 Summary

    4. 3.3 The Law of Cosines

      1. Algebra Refresher
      2. Law of Cosines
      3. Finding a Side
      4. Finding an Angle
      5. Using the Law of Cosines for the Ambiguous Case
      6. Application: Navigation
      7. Which Law to Use
      8. Section 3.3 Summary

    5. Chapter 3 Summary and Review

    6. Exercises: 3.1 Obtuse Angles

    7. Exercises: 3.2 The Law of Sines

    8. Exercises: 3.3 The Law of Cosines

    9. Exercises: Chapter 3 Review Problems

  6. Chapter 4: Trig Functions

    1. Introduction to Trigonometric Functions

      1. Introduction
      2. Class Activities

    2. 4.1 Angles and Rotation

      1. Algebra Refresher
      2. Angles in Standard Position
      3. Trigonometric Ratios for All Angles
      4. Reference Angles
      5. Using Reference Angles
      6. Coterminal Angles
      7. Solving Trigonometric Equations
      8. The Special Angles
      9. The Unit Circle
      10. Section 4.1 Summary

    3. 4.2 Graphs of Trigonometric Functions

      1. Algebra Refresher
      2. Location by Coordinates
      3. Bearings
      4. Function Notation
      5. The Tangent Function
      6. Angle of Inclination
      7. Section 4.2 Summary

    4. 4.3 Periodic Functions

      1. Algebra Refresher
      2. Period, Midline, and Amplitude
      3. Sinusoidal Functions
      4. Other Periodic Functions
      5. Section 4.3 Summary

    5. Chapter 4 Summary and Review

    6. Exercises: 4.1 Angles and Rotation

      1. Skills
      2. Exercises Homework 4.1

    7. Exercises: 4.2 Graphs of Trigonometric Functions

      1. Skills
      2. Homework 4.2

    8. Exercises: 4.3 Periodic Functions

      1. Skills
      3. Exercises Homework

    9. Exercises: Chapter 4 Review Problems

  7. Chapter 5: Equations and Identities

    1. Introduction to Equations and Identities

      1. Introduction

    2. 5.1 Algebra with Trigonometric Ratios

      1. Algebra Refresher
      2. Evaluating Trigonometric Expressions
      3. Simplifying Trigonometric Expressions
      4. Powers of Trigonometric Ratios
      5. Products
      6. Factoring
      7. Section 5.1 Summary

    3. 5.2 Solving Equations

      1. Algebra Refresher
      2. Trigonometric Equations
      3. Graphical Solutions
      4. Equations with Squares of Trig Ratios
      5. Snell’s Law
      6. Section 5.2 Summary

    4. 5.3 Trigonometric Identities

      1. Algebra Refresher
      2. Using Trigonometric Ratios in Identities
      3. Pythagorean Identity
      4. Tangent Identity
      5. Solving Equations
      6. Proving Identities
      7. Section 5.3 Summary

    5. Chapter 5 Summary and Review

    6. Exercises: 5.1 Algebra with Trigonometric Ratios

      1. Skills
      3. Exercises Homework 5.1

    7. Exercises: 5.2 Solving Equations

      1. Skills
      3. Exercises Homework 5.2

    8. Exercises: 5.3 Trigonometric Identities

      1. Skills
      3. Exercises Homework 5.3

    9. Exercises: Chapter 5 Review Problems

      2. Exercises for Chapter 5 Review
  8. Chapter 6: Radians

    1. Introduction to Trig Radians

      1. Introduction
      2. Class Activities

    2. 6.1 Arclength and Radians

      1. Algebra Refresher
      2. Arclength and Radians
      3. Arclength
      4. Measuring Angles in Radians
      5. Converting between Degrees and Radians
      6. Arclength Formula
      7. Unit Circle
      8. Section 6.1 Summary

    3. 6.2 The Circular Functions

      1. Algebra Refresher
      2. Trigonometric Functions of Angles in Radians
      3. Values of Special Angles
      4. Reference Angles in Radians
      5. Sine and Cosine of Real Numbers
      6. Coordinates on a Unit Circle
      7. The Tangent Function
      8. The Circular Functions
      9. Section 6.2 Summary

    4. 6.3 Graphs of the Circular Functions

      1. Algebra Refresher
      2. The Sine and Cosine Functions
      3. The Tangent Function
      4. Solving Equations
      5. Modeling with Circular Functions
      6. Domain and Range
      7. Section 6.3 Summary

    5. Chapter 6 Summary and Review

    6. Exercises 6.1 Arclength and Radians

    7. Exercises 6.2 The Circular Functions

    8. Exercises 6.3 Graphs of the Circular Functions

    9. Exercises: Chapter 6 Review Problems

  9. Chapter 7: Circular Functions

    1. Introduction to Circular Functions

      1. Introduction
      2. Class Activities

    2. 7.1 Transformations of Graphs

      1. Algebra Refresher
      2. Transformations of Graphs
      3. Graphs of Sinusoidal Functions
      4. Modeling with Sinusoidal Functions
      5. The Tangent Function
      6. Section 7.1 Summary

    3. 7.2 The General Sinusoidal Function

      1. Algebra Refresher
      2. The General Sinusoidal Function
      3. Combining Transformations
      4. Modeling with Sinusoidal Functions
      5. Section 7.2 Summary

    4. 7.3 Solving Equations

      1. Algebra Refresher
      2. Multiple Solutions
      3. Using a Substitution
      4. Applications
      5. Section 7.3 Summary

    5. Chapter 7 Summary and Review

    6. Exercises 7.1 Transformations of Graphs

    7. Exercises 7.2 The General Sinusoidal Function

    8. Exercises 7.3 Solving Equations

    9. Exercises: Chapter 7 Review Problems

  10. Chapter 8: More Functions and Identities

    1. Introduction to More Functions and Identities

      1. Introduction
      2. Class Activities

    2. 8.1 Sum and Difference Formulas

      1. Algebra Refresher
      2. The Sum of Angles Identities
      3. The Difference of Angles Identities
      4. Sum and Difference Identities for Tangent
      5. Double Angle Identities
      6. Solving Equations
      7. Section 8.1 Summary

    3. 8.2 Inverse Trigonometric Functions

      1. Algebra Refresher
      3. Inverse of a Function
      4. The Graph of the Inverse
      5. The Inverse Cosine and Inverse Tangent Functions
      6. Modeling with Inverse Functions
      7. Simplifying Inverse Expressions
      8. Section 8.2 Summary

    4. 8.3 The Reciprocal Functions

      1. Algebra Refresher
      2. Three More Functions
      3. Application to Right Triangles
      4. Graphs of the Reciprocal Functions
      5. Solving Equations
      6. Using Identities
      7. Section 8.3 Summary

    5. Chapter 8 Summary and Review

    6. Exercises: 8.1 Sum and Difference Formulas

    7. Exercises: 8.2 Inverse Trigonometric Functions Exercises

    8. Exercises: 8.3 The Reciprocal Functions Exercises

    9. Exercises: Chapter 8 Review Problems

  11. Chapter 9: Vectors

    1. Introduction to Vectors

      1. Introduction

    2. 9.1 Geometric Form

      1. Skills Refresher
      2. Notation for Vectors
      3. Scalar Multiplication of Vectors
      4. Addition of Vectors
      5. Velocity
      6. Components of a Vector
      7. Using Components
      8. Section 9.1 Summary

    3. 9.2 Coordinate Form

      1. Skills Refresher
      2. Unit Vectors
      3. Converting between Geometric and Coordinate Form
      4. Scalar Multiples of Vectors in Coordinate Form
      5. Adding Vectors in Coordinate Form
      6. Force
      7. Section 9.2 Summary

    4. 9.3 The Dot Product

      1. Skills Refresher
      2. Components
      3. Coordinate Form for Components
      4. The Dot Product
      5. Geometric Meaning of the Dot Product
      6. Section 9.3 Summary

    5. Chapter 9 Summary and Review

    6. Exercises: 9.1 Geometric Form

    7. Exercises: 9.2 Coordinate Form

    8. Exercises: 9.3 The Dot Product

    9. Exercises: Chapter 9 Review Problems

  12. Chapter 10: Polar Coordinates and Complex Numbers

    1. Introduction to Polar Coordinates and Complex Numbers

      1. Introduction

    2. 10.1 Polar Coordinates

      1. Algebra Refresher
      2. Plotting Points
      3. Regions in the Plane
      4. Converting between Polar and Cartesian Coordinates
      5. Equations in Polar Coordinates
      6. Section 10.1 Summary

    3. 10.2 Polar Graphs

      1. Algebra Refresher
      2. Graphing in Polar Coordinates
      3. Sketching Familiar Equations
      4. Finding Intersection Points
      5. Section 10.2 Summary

    4. 10.3 Complex Numbers

      1. Algebra Refresher
      2. Imaginary Numbers
      3. Complex Numbers
      4. Arithmetic of Complex Numbers
      5. Products of Complex Numbers
      6. Quotients of Complex Numbers
      7. Graphing Complex Numbers
      8. Zeros of Polynomials
      9. Section 10.3 Summary

    5. 10.4 Polar Form for Complex Numbers

      1. Algebra Refresher
      2. Polar Form
      3. Products and Quotients in Polar Form
      4. Powers and Roots of Complex Numbers
      5. Section 10.4 Summary

    6. Chapter 10 Summary and Review

    7. Exercises: 10.1 Polar Coordinates

    8. Exercises: 10.2 Polar Graphs

    9. Exercises: 10.3 Complex Numbers

    10. Exercises: 10.4 Polar Form of Complex Numbers

    11. Exercises: Chapter 10 Review Problems

  13. Glossary

  14. Summary of Adaptations

    1. Full Resource Adaptations
    2. Chapter-Specific Changes