OER Math 1060 - Trigonometry - Pilot Edition - Spring 2017

Sep 14, 2026

Uploaded by Logic

OER Math 1060 - Trigonometry (Pilot Edition, Spring 2017) provides an openly accessible learning resource for college-level trigonometry. The material starts with angle measure, covering degree and radian systems, conversions, supplementary and complementary relationships, and applications tied to circular arc length and speed. Subsequent chapters develop right-triangle trigonometry, unit-circle values, trigonometric function graphs, identities and formulas, inverse functions, and strategies for solving trigonometric equations. Later topics extend to triangles via the Law of Sines and Cosines, polar coordinates, and vectors with parametric equations.

LanguageEnglish

CategoryExam

FormatPDF

Pages471

Reading Time19 h 47 min

AccessFree to download

Chapter 1 Angles and Their Measure

1.1 Degree Measure of Angles

1.2 Radian Measure of Angles

1.3 Applications of Radian Measure

Chapter 2 The Trigonometric Functions

2.1 Right Triangle Trigonometry

2.2 Determining Cosine and Sine Values from the Unit Circle

2.3 The Six Circular Functions

2.4 Verifying Trigonometric Identities

2.5 Beyond the Unit Circle

Chapter 3 Graphs of the Trigonometric Functions

3.1 Graphs of the Cosine and Sine Functions

3.2 Properties of the Graphs of Sinusoids

3.3 Graphs of the Tangent and Cotangent Functions

3.4 Graphs of the Secant and Cosecant Functions

Chapter 4 Trigonometric Identities and Formulas

4.1 The Even/Odd Identities

4.2 The Sum and Difference Identities

4.3 Double Angle Identities

4.4 Power Reduction and Half Angle Formulas

4.5 Product to Sum and Sum to Product Formulas

4.6 Using Sum Identities in Determining Sinusoidal Formulas

Chapter 5 The Inverse Trigonometric Functions

5.1 Properties of the Inverse Cosine and Sine Functions

5.2 Properties of the Inverse Tangent and Cotangent Functions

5.3 Properties of the Inverse Secant and Cosecant Functions

5.4 Calculators and the Inverse Circular Functions

Chapter 6 Trigonometric Equations

6.1 Solving Equations Using the Inverse Trigonometric Functions

6.2 Solving Equations Involving a Single Trigonometric Function

6.3 Solving Equations of Multiple Trigonometric Functions/Arguments

Chapter 7 Beyond Right Triangles

7.1 Solving Triangles with the Law of Sines

7.2 Applications of the Law of Sines

7.3 The Law of Cosines

Chapter 8 Polar Coordinates and Applications

8.1 Polar Coordinates

8.2 Polar Equations

8.3 Graphing Polar Equations

8.4 Polar Representations for Complex Numbers

8.5 Complex Products, Powers, Quotients and Roots

Chapter 9 Vectors and Parametric Equations

9.1 Vector Properties and Operations

9.2 The Unit Vector and Vector Applications

9.3 The Dot Product

9.4 Sketching Curves Described by Parametric Equations

9.5 Finding Parametric Descriptions for Oriented Curves

OER Math 1060 – Trigonometry Pilot Edition Spring 2017 Salt Lake Community College & University of Utah Acknowledgements Content is based on College Trigonometry, 3rd Corrected Edition by Carl Stitz and Jeffrey Zeager, to whom we are grateful beyond words for their dedication in creating and sharing their OER textbook. This textbook has been developed by Ruth Trygstad, Salt Lake Community College (SLCC), with contributions from Shawna Haider (SLCC), Spencer Bartholomew (SLCC) and Maggie Cummings (University of Utah) . Many additional faculty and staff from both Salt Lake Community College and the University of Utah have helped with this pilot edition. The project has been sponsored and supported by SLCC, the SLCC Math Department and the University of Utah Math Department. Special thanks goes to Jason Pickavance, Suzanne Mozdy and Peter Trapa for their encouragement. Additional content, including Exercises, has been borrowed from OpenStax College, Algebra and Trigonometry, [openstaxcollege.org/textbooks/college](openstaxcollege.org/textbooks/college)algebra-and-trigonometry. CHAPTER 1 ANGLES AND THEIR MEASURE 1 1.1 Degree Measure of Angles 2 1.1 Exercises 12 1.2 Radian Measure of Angles 13 1.2 Exercises 19 1.3 Applications of Radian Measure 20 1.3 Exercises 29 CHAPTER 2 THE TRIGONOMETRIC FUNCTIONS 31 2.1 Right Triangle Trigonometry 32 2.1 Exercises 45 2.2 Determining Cosine and Sine Values from the Unit Circle 53 2.2 Exercises 71 2.3 The Six Circular Functions 73 2.3 Exercises 85 2.4 Verifying Trigonometric Identities 87 2.4 Exercises 93 2.5 Beyond the Unit Circle 95 2.5 Exercises 102 CHAPTER 3 GRAPHS OF THE TRIGONOMETRIC FUNCTIONS 104 3.1 Graphs ofthe Cosine and Sine Functions 105 3.1 Exercises 117 3.2 Properties of the Graphs of Sinusoids 119 3.2 Exercises 135 3.3 Graphs ofthe Tangent and Cotangent Functions 140 3.3 Exercises 151 3.4 Graphs of the Secant and Cosecant Functions 153 3.4 Exercises 163 CHAPTER 4 TRIGONOMETRIC IDENTITIES AND FORMULAS 166 4.1 The Even/Odd Identities 167 4.1 Exercises 170 4.2 The Sum and Difference Identities 171 4.2 Exercises 181 4.3 Double Angle Identities 183 4.3 Exercises 189 4.4 Power Reduction and Half Angle Formulas 191 4.4 Exercises 196 4.5 Product to Sum and Sum to Product Formulas 198 4.5 Exercises 201 4.6 Using Sum Identities in Determining Sinusoidal Formulas 202 4.6 Exercises 206 CHAPTER 5 THE INVERSE TRIGONOMETRIC FUNCTIONS 207 5.1 Properties of the Inverse Cosine and Sine Functions 208 5.1 Exercises 217 5.2 Properties of the Inverse Tangent and Cotangent Functions 219 5.2 Exercises 226 5.3 Properties of the Inverse Secant and Cosecant Functions 228 5.3 Exercises 234 5.4 Calculators and the Inverse Circular Functions 236 5.4 Exercises 244 CHAPTER 6 TRIGONOMETRIC EQUATIONS 246 6.1 Solving Equations Using the Inverse Trigonometric Functions 247 6.1 Exercises 253 6.2 Solving Equations Involving a Single Trigonometric Function 254 6.2 Exercises 263 6.3 Solving Equations of Multiple Trigonometric Functions/Arguments 264 6.3 Exercises 271 CHAPTER 7 BEYOND RIGHT TRIANGLES 273 7.1 Solving Triangles with the Law of Sines 274 7.1 Exercises 287 7.2 Applications of the Law of Sines 291 7.2 Exercises 296 7.3 The Law of Cosines 302 7.3 Exercises 311 CHAPTER 8 POLAR COORDINATES AND APPLICATIONS 317 8.1 Polar Coordinates 318 8.1 Exercises 334 8.2 Polar Equations 336 8.2 Exercises 342 8.3 Graphing Polar Equations 343 8.3 Exercises 360 8.4 Polar Representations for Complex Numbers 362 8.4 Exercises 373 8.5 Complex Products, Powers, Quotients and Roots 375 8.5 Exercises 387 CHAPTER 9 VECTORS AND PARAMETRIC EQUATIONS 390 9.1 Vector Properties and Operations 391 9.1 Exercises 405 9.2 The Unit Vector and Vector Applications 410 9.2 Exercises 419 9.3 The Dot Product 422 9.3 Exercises 437 9.4 Sketching Curves Described by Parametric

FAQs

What topics are covered in Chapter 1 of OER Math 1060 - Trigonometry?

Chapter 1 focuses on angles and their measure, including degree measure, radian measure, and applications of radian measure such as circular arc length, area, and motion-related speed.

How does the textbook develop understanding of trigonometric functions?

It begins with right-triangle trigonometry, then extends to unit-circle values, the six circular functions, and verification of trigonometric identities, followed by work beyond the unit circle.

What advanced areas are included after trigonometric equations?

The later chapters address beyond-right-triangle solving using the Law of Sines and Law of Cosines, polar coordinates and their applications, and vectors and parametric equations.

Sep 14, 2026

Uploaded by Logic