Trigonometry Collected Resources

Janice Podgurski, Jun 10, 2024

A resource covering all aspects of Trigonometry. This collection was my senior project for my degree in Mathematics. I have collected resources that were already out there, a lot of Tim Brezsinski's Trig modules, some from the GeoGebra Content team, and a few others that were exceptional. Then with my faculty advisor, I set out to create some content that I felt was lacking. This resource can be used to learn Trig, teach Trig, or just freshen up or expand your knowledge in the area. This book is a work in progress, and will be added to as I find and/or create new quality stuff.

Table of Contents

  1. Basic Geometric Concepts
    1. Basic Objects
    2. Measuring Angles
    3. Radian Measure of Rotational Angles
    4. Guess the Radian Measure
    5. Measuring Angles
    6. Drawing Angles Game
    7. Determining Angle Measures Without Tools
    8. Exploring Parts of an Angle
    9. Identifying Angles Around Us
  2. Basic Triangle Properties
    1. Classifying Triangles in Euclidean Geometry
    2. Sum of Interior Angles of a Triangle
  3. Triangle Congruence & Similarity
    1. Triangle Congruence
    2. SAS Triangle Congruence Exploration Euclidean Geometry
    3. SAS: Dynamic Proof!
    4. SAS Triangle Similarity Theorem
    5. SAS Similarity Theorem: Exploration
    6. ASA Theorem?
    7. ASA Triangle Congruence Exploration Euclidean Geometry
    8. ASA Triangle Congruence Theorem Proof
    9. Angle-Side-Angle (ASA): Quick Exploration
    10. SSS Triangle Congruence Exploration Euclidean Geometry
    11. SSS Triangle Exploration
    12. SSS ~ Theorem (V1)
    13. SSS ~ Theorem (V2)
    14. SSS: Dynamically Illustrated
    15. AAS Triangle Congruence Exploration Euclidean Geometry
    16. Angle-Angle-Side (AAS): Quick Exploration
    17. AAS Triangle Congruence Exploration Euclidean Geometry
    18. SSA Theorem?
    19. SSA Triangle Congruence Exploration Euclidean Geometry
    20. AAA Triangle Exploration Euclidean Geometry
    21. AA Similarity Theorem
  4. Right Triangle Trigonometry
    1. Defining the Sine, Cosine, and Tangent
    2. Special Triangles
    3. Right Triangle Trig Intro and Exploration (2)
    4. Right Triangle Trig Intro and Exploration (2)
    5. "SOH-CAH-TOA" FAILED to Show You This
    6. Thinking Classroom Exploration: Using Trig Ratios to Solve for Sides of Right Triangles
    7. Right Triangle Trig Intro and Exploration
    8. Right Triangle Trig: Solving for Sides
    9. Right Triangle Trig: Solving for Sides (2)
    10. Right Triangle Trig: Solving for Sides
    11. 4Q Quiz: Right Triangle Trig - Solving for Sides
    12. Basic Trigonometry with a Right Angled Triangle
    13. Investigating Trigonometry Ratios
    14. New Trig ID's from Similar Right Triangles (V2)
    15. New Trig IDs From Similar Right Triangles
    16. Investigating Trigonometry Ratios
    17. Definition of Trigonometry
    18. Trigonometry Tracer
    19. Trigonometry-Area Formula
    20. Trigonometry ASTC introduction
    21. Trigonometry Investigation
    22. Trig Function Values (30 Degrees)
    23. Trig Function Values (60 Degrees)
    24. Trig Function Values (45 Degrees)
    25. 4Q Quiz: Identifying Trig Ratios
    26. 4Q Quiz: Identifying Trig Ratios
    27. Trig Ratio Estimations (Quiz: V2)
  5. Circular Trigonometric Functions
    1. Circular Trig Functions
    2. The Unit Circle (Part 1)
    3. The Unit Circle (Part 2)
    4. Trigonometry Reference
    5. Trig Circle Start: Multiples of 30°
    6. Trig Circle: Coordinates of Special Angle Values
    7. Unit circle for trigonometry.
    8. Trig Reference Circle: Choose Your Own Radius
    9. Trig Reference Circle (2): Choose Your Own Radius
    10. Trigonometry with unit circle
    11. Quiz: Quadrant Logic (Trig)
    12. 4Q Quiz: Quadrant Logic (Trig)
    13. Trig Quadrant Logic (2)
    14. Evaluating Trig Functions Given a Point on the Terminal Ray
  6. Graphing Trigonometric Functions
    1. Graphing Basic Trig Functions
    2. Open Middle: Graphing Trig Functions Exercise
    3. Open Middle: Graphing Trig Functions Exercise (2)
    4. Graphing and Transforming Trigonometry Functions
    5. Investigating Trigonometry Graph Transformations
    6. 4 Parent Trig Functions
    7. Trigonometry function
    8. The Trigonometry Functions
    9. Open Middle: Build a Trig Equation (1)
    10. Open Middle: Build a Trig Equation (2)
    11. Open Middle: Build a Trig Equation (3)
    12. Open Middle: Build a Trig Equation (4)
    13. Open Middle: Build a Trig Equation (5)
    14. Open Middle: Build a Trig Equation (6)
    15. Open Middle: Build a Trig Equation (7)
    16. Open Middle: Build a Trig Equation (8)
    17. Basic Trig Graphing Open Middle Problem
    18. Basic Trig Graphing Open Middle Problem
  7. Trigonometric Identities
    1. Double Angle Trig Identity: Proof via Equal Areas
    2. Trig Identity Shown Graphically
    3. Trigonometric identities: Part I
    4. Trigonometric identities: Part II
    5. Trigonometric identities: Part III
    6. Special Trigonometric Identities: Quick Exploration
    7. Tangent of a Difference: Trig Identity Puzzle + Proof!
    8. Trig ID Movie (II)
    9. Trig ID Movie (III)
    10. Trig Identity (3) - Geometric Investigation
    11. Trig Identity (4) - Geometric Investigation
    12. A Very Unusual Trig Identity
    13. Trig Identities from Similar Right Triangles (I)
    14. Pythagorean Trigonometric Identity (1)
    15. Proofs in Trigonometric Identities Practice : Scaffolded with Drag n Drop
    16. Another Popular Trig Identity
    17. New Trig ID's from Similar Right Triangles (V2)
    18. New Trig IDs From Similar Right Triangles
    19. Trig Identity via Areas (2): Dynamic Illustrator
    20. Trig Identities from Similar Right Triangles (II)
    21. Bizzare Trig Identity?
    22. Trig Identity via Areas: Dynamic Illustrator
    23. Trig ID: Geometric Investigation
  8. Inverse Trigonometric Functions
    1. Using Inverse Trig Functions to Express Angle Measures
    2. Evaluating Inverse Trig Functions of Special Ratios
    3. 4Q Quiz: Evaluating Inverse Trig Functions of Special Ratios
    4. 4Q Quiz: Using Inverse Trig Functions to Express Angle Measures
    5. Compositions of Trig & Inverse Trig Functions (1)
    6. Evaluating Compositions of Trig & Inverse Trig Functions (2)
    7. 4Q Quiz: Compositions of Trig & Inverse Trig Functions (1)
    8. Inverse Trig Functions: Intuitive Explorations
  9. Solving General Triangles
  10. Trigonometric Equations and Inequalities
  11. Vectors
    1. Normal Vector
    2. Vector Addition
    3. Vector Subtraction
    4. Vector Projection
    5. Vector Projections (1)
    6. Scaling Vectors
    7. 2D Scalar times Vector
    8. 2D Vector Sum, Scalar Multiple, Linear Combination
    9. 3D Vector Components: Dynamic Illustrator
    10. Battleship in the Coordinate Plane!
  12. Polar Coordinates
  13. Complex Numbers
  14. Applications

1.

Basic Geometric Concepts

Introducing the most basic geometric concepts needed for a foundation in Trigonometry. Ray, Angle Measuring Angles, Radians, Degrees, DMS

  • 1. Basic Objects
  • 2. Measuring Angles
  • 3. Radian Measure of Rotational Angles
  • 4. Guess the Radian Measure
  • 5. Measuring Angles
  • 6. Drawing Angles Game
  • 7. Determining Angle Measures Without Tools
  • 8. Exploring Parts of an Angle
  • 9. Identifying Angles Around Us

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1.6.

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1.9.

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2.

Basic Triangle Properties

Exploring triangle classification and their properties. Defining and Classifying Triangles Triangle Inequality Angle Sum Theorem

  • 1. Classifying Triangles in Euclidean Geometry
  • 2. Sum of Interior Angles of a Triangle

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3.

Triangle Congruence & Similarity

Exploring triangle congruence properties and theorems and similarity of triangles. SAS Postulate, ASA, AAS, and SSS Congruence Theorems SSA Condition AA, SAS and SSS Triangle Similarity Theorems

  • 1. Triangle Congruence
  • 2. SAS Triangle Congruence Exploration Euclidean Geometry
  • 3. SAS: Dynamic Proof!
  • 4. SAS Triangle Similarity Theorem
  • 5. SAS Similarity Theorem: Exploration
  • 6. ASA Theorem?
  • 7. ASA Triangle Congruence Exploration Euclidean Geometry
  • 8. ASA Triangle Congruence Theorem Proof
  • 9. Angle-Side-Angle (ASA): Quick Exploration
  • 10. SSS Triangle Congruence Exploration Euclidean Geometry
  • 11. SSS Triangle Exploration
  • 12. SSS ~ Theorem (V1)
  • 13. SSS ~ Theorem (V2)
  • 14. SSS: Dynamically Illustrated
  • 15. AAS Triangle Congruence Exploration Euclidean Geometry
  • 16. Angle-Angle-Side (AAS): Quick Exploration
  • 17. AAS Triangle Congruence Exploration Euclidean Geometry
  • 18. SSA Theorem?
  • 19. SSA Triangle Congruence Exploration Euclidean Geometry
  • 20. AAA Triangle Exploration Euclidean Geometry
  • 21. AA Similarity Theorem

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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3.16.

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3.17.

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3.18.

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3.19.

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3.20.

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3.21.

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4.

Right Triangle Trigonometry

Pythagorean Theorem Angle Sum Theorem Trig Functions of an Acute Angle Trig Functions of Special Angles Area of a Triangle Solving Right Triangles

  • 1. Defining the Sine, Cosine, and Tangent
  • 2. Special Triangles
  • 3. Right Triangle Trig Intro and Exploration (2)
  • 4. Right Triangle Trig Intro and Exploration (2)
  • 5. "SOH-CAH-TOA" FAILED to Show You This
  • 6. Thinking Classroom Exploration: Using Trig Ratios to Solve for Sides of Right Triangles
  • 7. Right Triangle Trig Intro and Exploration
  • 8. Right Triangle Trig: Solving for Sides
  • 9. Right Triangle Trig: Solving for Sides (2)
  • 10. Right Triangle Trig: Solving for Sides
  • 11. 4Q Quiz: Right Triangle Trig - Solving for Sides
  • 12. Basic Trigonometry with a Right Angled Triangle
  • 13. Investigating Trigonometry Ratios
  • 14. New Trig ID's from Similar Right Triangles (V2)
  • 15. New Trig IDs From Similar Right Triangles
  • 16. Investigating Trigonometry Ratios
  • 17. Definition of Trigonometry
  • 18. Trigonometry Tracer
  • 19. Trigonometry-Area Formula
  • 20. Trigonometry ASTC introduction
  • 21. Trigonometry Investigation
  • 22. Trig Function Values (30 Degrees)
  • 23. Trig Function Values (60 Degrees)
  • 24. Trig Function Values (45 Degrees)
  • 25. 4Q Quiz: Identifying Trig Ratios
  • 26. 4Q Quiz: Identifying Trig Ratios
  • 27. Trig Ratio Estimations (Quiz: V2)

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4.11.

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4.12.

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4.13.

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4.14.

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4.15.

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4.16.

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4.17.

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4.18.

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4.19.

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4.20.

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4.21.

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4.22.

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4.23.

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4.24.

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4.25.

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4.26.

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4.27.

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5.

Circular Trigonometric Functions

Extending definitions of Sin and Cosine to include any real number input. Defining Trig Functions for +/- Rotational Angles. Unit Circle Periodic Properties Symmetry Properties

  • 1. Circular Trig Functions
  • 2. The Unit Circle (Part 1)
  • 3. The Unit Circle (Part 2)
  • 4. Trigonometry Reference
  • 5. Trig Circle Start: Multiples of 30°
  • 6. Trig Circle: Coordinates of Special Angle Values
  • 7. Unit circle for trigonometry.
  • 8. Trig Reference Circle: Choose Your Own Radius
  • 9. Trig Reference Circle (2): Choose Your Own Radius
  • 10. Trigonometry with unit circle
  • 11. Quiz: Quadrant Logic (Trig)
  • 12. 4Q Quiz: Quadrant Logic (Trig)
  • 13. Trig Quadrant Logic (2)
  • 14. Evaluating Trig Functions Given a Point on the Terminal Ray

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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5.14.

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6.

Graphing Trigonometric Functions

Obtaining Cartesian Graphs of Trigonometric Functions from Unit Circle representation. Transforming Trigonometric Graphs.

  • 1. Graphing Basic Trig Functions
  • 2. Open Middle: Graphing Trig Functions Exercise
  • 3. Open Middle: Graphing Trig Functions Exercise (2)
  • 4. Graphing and Transforming Trigonometry Functions
  • 5. Investigating Trigonometry Graph Transformations
  • 6. 4 Parent Trig Functions
  • 7. Trigonometry function
  • 8. The Trigonometry Functions
  • 9. Open Middle: Build a Trig Equation (1)
  • 10. Open Middle: Build a Trig Equation (2)
  • 11. Open Middle: Build a Trig Equation (3)
  • 12. Open Middle: Build a Trig Equation (4)
  • 13. Open Middle: Build a Trig Equation (5)
  • 14. Open Middle: Build a Trig Equation (6)
  • 15. Open Middle: Build a Trig Equation (7)
  • 16. Open Middle: Build a Trig Equation (8)
  • 17. Basic Trig Graphing Open Middle Problem
  • 18. Basic Trig Graphing Open Middle Problem

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6.9.

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6.10.

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6.11.

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6.12.

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6.13.

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6.14.

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6.15.

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6.16.

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6.17.

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6.18.

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7.

Trigonometric Identities

Illustrating and proving Trigonometric Identities

  • 1. Double Angle Trig Identity: Proof via Equal Areas
  • 2. Trig Identity Shown Graphically
  • 3. Trigonometric identities: Part I
  • 4. Trigonometric identities: Part II
  • 5. Trigonometric identities: Part III
  • 6. Special Trigonometric Identities: Quick Exploration
  • 7. Tangent of a Difference: Trig Identity Puzzle + Proof!
  • 8. Trig ID Movie (II)
  • 9. Trig ID Movie (III)
  • 10. Trig Identity (3) - Geometric Investigation
  • 11. Trig Identity (4) - Geometric Investigation
  • 12. A Very Unusual Trig Identity
  • 13. Trig Identities from Similar Right Triangles (I)
  • 14. Pythagorean Trigonometric Identity (1)
  • 15. Proofs in Trigonometric Identities Practice : Scaffolded with Drag n Drop
  • 16. Another Popular Trig Identity
  • 17. New Trig ID's from Similar Right Triangles (V2)
  • 18. New Trig IDs From Similar Right Triangles
  • 19. Trig Identity via Areas (2): Dynamic Illustrator
  • 20. Trig Identities from Similar Right Triangles (II)
  • 21. Bizzare Trig Identity?
  • 22. Trig Identity via Areas: Dynamic Illustrator
  • 23. Trig ID: Geometric Investigation

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7.11.

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8.

Inverse Trigonometric Functions

Defining and Graphing Inverse Trigonometric Functions Properties of Inverse Trigonometric Functions

  • 1. Using Inverse Trig Functions to Express Angle Measures
  • 2. Evaluating Inverse Trig Functions of Special Ratios
  • 3. 4Q Quiz: Evaluating Inverse Trig Functions of Special Ratios
  • 4. 4Q Quiz: Using Inverse Trig Functions to Express Angle Measures
  • 5. Compositions of Trig & Inverse Trig Functions (1)
  • 6. Evaluating Compositions of Trig & Inverse Trig Functions (2)
  • 7. 4Q Quiz: Compositions of Trig & Inverse Trig Functions (1)
  • 8. Inverse Trig Functions: Intuitive Explorations

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9.

Solving General Triangles

Law of Sines & Law of Cosines


    This chapter does not contain any resources yet.

10.

Trigonometric Equations and Inequalities

Solving Trigonometric Equations and Inequalities


    This chapter does not contain any resources yet.

11.

Vectors

Defining Vectors Magnitude and Direction <-> Component Form Vector Operations: addition, subtraction, scalar multiple, dot product, cross product.

  • 1. Normal Vector
  • 2. Vector Addition
  • 3. Vector Subtraction
  • 4. Vector Projection
  • 5. Vector Projections (1)
  • 6. Scaling Vectors
  • 7. 2D Scalar times Vector
  • 8. 2D Vector Sum, Scalar Multiple, Linear Combination
  • 9. 3D Vector Components: Dynamic Illustrator
  • 10. Battleship in the Coordinate Plane!

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12.

Polar Coordinates

Defining Polar Coordinates Graphing Polar Functions


    This chapter does not contain any resources yet.

13.

Complex Numbers

Defining and Graphing Complex numbers Complex Number Operations: Addition, subtraction, multiplication, division, and powers.


    This chapter does not contain any resources yet.

14.

Applications


    This chapter does not contain any resources yet.

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