## Summary

Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts. Written in a readable, yet mathematically mature manner appropriate for college level students, Coburn's Trigonometry uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn's hallmark applications are born out of the author's extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area. Benefiting from the feedback of hundreds of instructors and students across the country, Trigonometry, Second Edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in trigonometry.

## Table of Contents

# Coburn and Herdlick

# Trigonometry, 2e

## Chapter 1: Introduction to Trigonometry

#### 1.1 Angle Measure and Special Triangles

#### 1.2 Properties of Triangles; Similar Triangles

#### Mid-Chapter Check

#### RBC: More on Special Triangles

#### 1.3 Trigonometry: A View from the Coordinate Plane

#### 1.4 Fundamental Identities and Families of Identities

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery: The Range of Sine, Cosine, and Tangent

#### SCS: Creating New Identities

## Chapter 2: Right Triangles & Static Trigonometry

#### 2.1 A Right Triangle View of Trigonometry

#### 2.2 Solving Right Triangles

#### Mid-Chapter Check

#### RBC: The Area of a Triangle

#### 2.3 Applications of Static Trigonometry

#### 2.4 Extending Beyond Acute Angles

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery: Solving Triangles

#### SCS: Standard Angles, Reference Angles, and the Trig Functions

#### Cumulative Review 1 - 2

## Chapter 3: Radian Measure & Dynamic Trigonometry

#### 3.1 Angle Measure in Radians

#### 3.2 Arc Lengths, Velocities, and the Area of a Circular Sector

#### Mid-Chapter Check

#### RBC: More on Radians

#### 3.3 The Unit Circle

#### 3.4 The Trigonometry of Real Numbers

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery: Signs, Quadrants and Reference Arcs

#### SCS: Trigonometry of the Real Numbers and the Wrapping Function

#### Cumulative Review 1 - 3

## Chapter 4: Trigonometric Graphs and Models

#### 4.1 Graphs of Sine and Cosine Functions

#### 4.2 Graphs of Cosecant, Secant, Tangent and Cotangent Functions

#### Mid-Chapter Check

#### RBC: Trigonometric Potpourri

#### 4.3 Transformations of Trigonometric Graphs

#### 4.4 Trigonometric Applications and Models

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery

#### SCS

#### Cumulative Review 1 – 4

## Modeling With Technology: Trigonometric Equation Models

## Chapter 5: Trigonometric Identities

#### 5.1 More on Verifying Identities

#### 5.2 The Sum and Difference Identities

#### Mid-Chapter Check RBC: Understanding Identities

#### 5.3 The Double Angle and Half Angle Identities

#### 5.4 The Product-to-Sum and Sum-to-Product Identities

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery

#### SCS

#### Cumulative Review 1 - 5

## Chapter 6: Inverse Functions and Trigonometric Equations

#### 6.1 One-to-One and Inverse Functions

#### 6.2 Inverse Trigonometric Functions and their Applications

#### Mid -Chapter Check

#### RBC: More on Equation Solving

#### 6.3 Solving Basic Trigonometric Equations

#### 6.4 General Trigonometric Equations and Applications

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery

#### SCS: Trigonometric Equations and Inequalities

#### Cumulative Review 1 - 6

## Chapter 7: Applications of Trigonometry

#### 7.1 Oblique Triangles and the Law of Sines

#### 7.2 The Law of Cosines; the Area of a Triangle

#### Mid -Chapter Check

#### RBC

#### 7.3 Vectors and Vector Diagrams

#### 7.4 Vectors Applications and the Dot Product

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery

#### SCS

#### Cumulative Review 1 - 7

## Chapter 8: Trigonometric Connections to Algebra

#### 8.1 Complex Numbers

#### 8.2 Complex Numbers in Trigonometric Form

#### 8.3 Demoivre’s Theorem and the nth Roots Theorem

#### Mid-Chapter Check

#### RBC

#### 8.4 Polar Coordinates and Equations

#### 8.5 Graphs of Polar Equations

#### 8.6 Parametric Equations and Graphs

#### Summary/Concept Rev, Mixed Rev, Practice Test

#### Calc Exploration and Discovery

#### SCS

#### Cumulative Review 1 – 8

## Appendices

#### A.1 Exponential and Logarithmic Functions

#### A.2 Review and Technology

#### •Miscellaneous Algebra Review

#### •Transformations of Basic Graphs

#### •Solving Equations Graphically

#### •Regression and Calculator Use

#### •Families of Polar Graphs