Trigonometry Collected Resources

Janice Podgurski, Dr. Jack L. Jackson II, 6 août 2025

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, Dr. Jack Jackson, I set out to create some content that I felt was lacking. This resource can be used to learn Trigonometry, teach Trigonometry, or just freshen up or expand your knowledge in the area.

Table des matières

  1. Basic Geometric Concepts
    1. Basic Objects
    2. Exploring Parts of an Angle
    3. Identifying Angles Around Us
    4. Measuring Angles
    5. Radian Measure of Rotational Angles
    6. 1 Radian: Clear Definition
    7. Radian Illustrator
    8. Guess the Radian Measure
    9. Measuring Angles
    10. Drawing Angles Game
    11. Determining Angle Measures Without Tools
    12. Directional Vectors
    13. Angles in Standard Position
    14. Angle Orientations (Standard Position)
    15. Quiz: Sketching Angles in Standard Position
    16. 4Q Quiz: Sketching Angles in Standard Position
    17. Coterminal Angles Action!!!
    18. Coterminal Angles: Question Generator
    19. Relationship between area of sector, radius and angle (in degrees) slider version
  2. Basic Triangle Properties
    1. Euclidean General Triangle measured
    2. Classifying Triangles in Euclidean Geometry
    3. 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. ASA Triangle Congruence Exploration Euclidean Geometry
    5. Angle-Side-Angle (ASA): Quick Exploration
    6. ASA Theorem?
    7. ASA Triangle Congruence Theorem Proof
    8. AAS Triangle Congruence Exploration Euclidean Geometry
    9. Angle-Angle-Side (AAS): 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. SSA Triangle Congruence Exploration Euclidean Geometry
    16. SSA Theorem?
    17. AAA Triangle Exploration Euclidean Geometry
    18. AA Similarity Theorem
    19. SAS Triangle Similarity Theorem
    20. SAS Similarity Theorem: Exploration
    21. SSS Triangle Similarity Theorem
    22. 2 Noncongruent Triangles with 5 Congruent Parts
  4. Right Triangle Trigonometry
    1. Pythagorean Theorem
    2. Pythagorean Animation
    3. Pythagorean Theorem Animation
    4. Calculating Side Lengths in Right Triangles
    5. Calculating Distance Between Two Points on a Map
    6. Defining the Sine, Cosine, and Tangent
    7. "SOH-CAH-TOA" FAILED to Show You This
    8. Basic Trigonometry with a Right Angled Triangle
    9. Trig Functions without a Calculator
    10. Trigonometric Ratios in Right Triangles
    11. Trig Values Quiz
    12. Special Triangles
    13. Right Triangle Trig Intro and Exploration
    14. Right Triangle Trig: Solving for Sides
    15. Right Triangle Trig: Solving for Sides (2)
    16. Right Triangle Trig: Solving for Sides
    17. 4Q Quiz: Right Triangle Trig - Solving for Sides
    18. New Trig ID's from Similar Right Triangles (V2)
    19. New Trig IDs From Similar Right Triangles
    20. Trigonometry-Area Formula
    21. Trigonometry ASTC introduction
    22. Trigonometry Investigation
    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)
    28. Solving Right Triangles
  5. Circular Trigonometric Functions
    1. Circular Trig Functions
    2. Evaluating Trig Functions Given a Point on the Terminal Ray
    3. Trig Values Quiz
    4. Quiz: Quadrant Logic (Trig)
    5. 4Q Quiz: Quadrant Logic (Trig)
    6. Trig Quadrant Logic (2)
    7. Trig Functions as Lengths
    8. Trigonometric Functions of Special Angles
    9. The Unit Circle (Part 1)
    10. Trig Circle Start: Multiples of 30°
    11. Trig Circle: Coordinates of Special Angle Values
    12. Trig Reference Circle (2): Choose Your Own Radius
    13. Special Angles in Standard Position: Intro (V3)
    14. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    15. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
    16. Does R Matter?
    17. 4Q Quiz: Evaluating Trig FNS of Angles (Quadrant Logic)
    18. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
  6. Graphing Trigonometric Functions
    1. Graphing Basic Trig Functions
    2. Trigonometric Graphs: Cartesian Graph Characteristics
    3. Graphing Trig Functions of Special Angles
    4. Transforming Graphs of Trigonometric Functions
    5. Transforming Graphs of Functions
    6. 4 Parent Trig Functions
    7. Modeling with Trigonometric Functions
    8. Sine and Cosine Equations (Radians)
    9. Sine and Cosine Equations (Degrees)
    10. Sum and Difference of Functions
    11. Product of Functions
    12. Open Middle: Graphing Trig Functions Exercise
    13. Open Middle: Graphing Trig Functions Exercise (2)
    14. Open Middle: Build a Trig Equation (1)
    15. Open Middle: Build a Trig Equation (2)
    16. Open Middle: Build a Trig Equation (3)
    17. Open Middle: Build a Trig Equation (4)
    18. Open Middle: Build a Trig Equation (5)
    19. Open Middle: Build a Trig Equation (6)
    20. Open Middle: Build a Trig Equation (7)
    21. Open Middle: Build a Trig Equation (8)
    22. Basic Trig Graphing Open Middle Problem
    23. Basic Trig Graphing Open Middle Problem
    24. Important Trigonometric Limits
  7. Trigonometric Identities
    1. Trigonometric Identities via Symmetry of the Unit Circle
    2. Another Popular Trig Identity
    3. Pythagorean Trigonometric Identity (1)
    4. Trig Identity via Areas: Dynamic Illustrator
    5. Trig ID Movie (II)
    6. Trig Identity via Areas (2): Dynamic Illustrator
    7. Trig ID Movie (III)
    8. Cosine and Secant Functions (Special Property)
    9. Cosine Identity
    10. Sine Identity
    11. Tangent Identity
    12. Trig Identity Shown Graphically
    13. Trigonometry Angle Sum Identities
    14. Double and Half Angle Identities
    15. Double Angle Trig Identity: Proof via Equal Areas
    16. Trig Identity (4) - Geometric Investigation
    17. Trig ID: Geometric Investigation
    18. Trig Identity (3) - Geometric Investigation
    19. Trigonometric identities: Part I
    20. Trigonometric identities: Part II
    21. Trigonometric identities: Part III
    22. Special Trigonometric Identities: Quick Exploration
    23. Tangent of a Difference: Trig Identity Puzzle + Proof!
    24. A Very Unusual Trig Identity
    25. Trig Identities from Similar Right Triangles (I)
    26. Proofs in Trigonometric Identities Practice : Scaffolded with Drag n Drop
    27. New Trig ID's from Similar Right Triangles (V2)
    28. New Trig IDs From Similar Right Triangles
    29. Trig Identities from Similar Right Triangles (II)
    30. Bizzare Trig Identity?
    31. Bizzare Trig Identity?
    32. Double Angle Identity Activity
    33. Copy of Visual Proof of ASin+BCos Identity
    34. Trig identities 1
    35. Adding sinusoidal waves (AI HL 1.13)
  8. Inverse Trigonometric Functions
    1. Inverse Trigonometric Functions
    2. Inverse Trig Functions: Intuitive Explorations
    3. Using Inverse Trig Functions to Express Angle Measures
    4. Evaluating Inverse Trig Functions of Special Ratios
    5. 4Q Quiz: Evaluating Inverse Trig Functions of Special Ratios
    6. 4Q Quiz: Using Inverse Trig Functions to Express Angle Measures
    7. Compositions of Trig & Inverse Trig Functions (1)
    8. Evaluating Compositions of Trig & Inverse Trig Functions (2)
    9. 4Q Quiz: Compositions of Trig & Inverse Trig Functions (1)
    10. Graphing Inverse Trig Functions
  9. Trigonometric Equations and Inequalities
    1. Solving Trigonometric Equations
    2. Principle of Solving Simple Trigonometric Equations
    3. Trigonometric Equations(SEE)
  10. Solving General Triangles
    1. Law of Cosines
    2. Euclid II 12 The Law Of Cosines Obtuse
    3. The Law of Cosines
    4. Law of Cosines: Discovery
    5. Proof Without Words: Hunger's Law of Cosine Dissection
    6. Law of Cosines (Circle Proof)
    7. Law of Sines
    8. Law of Sines (& Area)
    9. Law of Sines (Illustrated)
    10. Law of Sines: Intro via Areas
    11. Solving Triangles
    12. Solve Oblique Quick Quiz
  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 Dot and Cross Product
    10. 3D Vector Components: Dynamic Illustrator
    11. Battleship in the Coordinate Plane!
    12. Entering Vectors
  12. Parametric Graphs
  13. Polar Coordinates
  14. Complex Numbers
  15. 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. Exploring Parts of an Angle
  • 3. Identifying Angles Around Us
  • 4. Measuring Angles
  • 5. Radian Measure of Rotational Angles
  • 6. 1 Radian: Clear Definition
  • 7. Radian Illustrator
  • 8. Guess the Radian Measure
  • 9. Measuring Angles
  • 10. Drawing Angles Game
  • 11. Determining Angle Measures Without Tools
  • 12. Directional Vectors
  • 13. Angles in Standard Position
  • 14. Angle Orientations (Standard Position)
  • 15. Quiz: Sketching Angles in Standard Position
  • 16. 4Q Quiz: Sketching Angles in Standard Position
  • 17. Coterminal Angles Action!!!
  • 18. Coterminal Angles: Question Generator
  • 19. Relationship between area of sector, radius and angle (in degrees) slider version

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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1.17.

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1.18.

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1.19.

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2.

Basic Triangle Properties

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

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

2.1.

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2.3.

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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. ASA Triangle Congruence Exploration Euclidean Geometry
  • 5. Angle-Side-Angle (ASA): Quick Exploration
  • 6. ASA Theorem?
  • 7. ASA Triangle Congruence Theorem Proof
  • 8. AAS Triangle Congruence Exploration Euclidean Geometry
  • 9. Angle-Angle-Side (AAS): 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. SSA Triangle Congruence Exploration Euclidean Geometry
  • 16. SSA Theorem?
  • 17. AAA Triangle Exploration Euclidean Geometry
  • 18. AA Similarity Theorem
  • 19. SAS Triangle Similarity Theorem
  • 20. SAS Similarity Theorem: Exploration
  • 21. SSS Triangle Similarity Theorem
  • 22. 2 Noncongruent Triangles with 5 Congruent Parts

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3.7.

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3.11.

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3.12.

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3.13.

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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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3.22.

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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. Pythagorean Theorem
  • 2. Pythagorean Animation
  • 3. Pythagorean Theorem Animation
  • 4. Calculating Side Lengths in Right Triangles
  • 5. Calculating Distance Between Two Points on a Map
  • 6. Defining the Sine, Cosine, and Tangent
  • 7. "SOH-CAH-TOA" FAILED to Show You This
  • 8. Basic Trigonometry with a Right Angled Triangle
  • 9. Trig Functions without a Calculator
  • 10. Trigonometric Ratios in Right Triangles
  • 11. Trig Values Quiz
  • 12. Special Triangles
  • 13. Right Triangle Trig Intro and Exploration
  • 14. Right Triangle Trig: Solving for Sides
  • 15. Right Triangle Trig: Solving for Sides (2)
  • 16. Right Triangle Trig: Solving for Sides
  • 17. 4Q Quiz: Right Triangle Trig - Solving for Sides
  • 18. New Trig ID's from Similar Right Triangles (V2)
  • 19. New Trig IDs From Similar Right Triangles
  • 20. Trigonometry-Area Formula
  • 21. Trigonometry ASTC introduction
  • 22. Trigonometry Investigation
  • 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)
  • 28. Solving Right Triangles

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4.24.

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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. Evaluating Trig Functions Given a Point on the Terminal Ray
  • 3. Trig Values Quiz
  • 4. Quiz: Quadrant Logic (Trig)
  • 5. 4Q Quiz: Quadrant Logic (Trig)
  • 6. Trig Quadrant Logic (2)
  • 7. Trig Functions as Lengths
  • 8. Trigonometric Functions of Special Angles
  • 9. The Unit Circle (Part 1)
  • 10. Trig Circle Start: Multiples of 30°
  • 11. Trig Circle: Coordinates of Special Angle Values
  • 12. Trig Reference Circle (2): Choose Your Own Radius
  • 13. Special Angles in Standard Position: Intro (V3)
  • 14. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
  • 15. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
  • 16. Does R Matter?
  • 17. 4Q Quiz: Evaluating Trig FNS of Angles (Quadrant Logic)
  • 18. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray

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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. Trigonometric Graphs: Cartesian Graph Characteristics
  • 3. Graphing Trig Functions of Special Angles
  • 4. Transforming Graphs of Trigonometric Functions
  • 5. Transforming Graphs of Functions
  • 6. 4 Parent Trig Functions
  • 7. Modeling with Trigonometric Functions
  • 8. Sine and Cosine Equations (Radians)
  • 9. Sine and Cosine Equations (Degrees)
  • 10. Sum and Difference of Functions
  • 11. Product of Functions
  • 12. Open Middle: Graphing Trig Functions Exercise
  • 13. Open Middle: Graphing Trig Functions Exercise (2)
  • 14. Open Middle: Build a Trig Equation (1)
  • 15. Open Middle: Build a Trig Equation (2)
  • 16. Open Middle: Build a Trig Equation (3)
  • 17. Open Middle: Build a Trig Equation (4)
  • 18. Open Middle: Build a Trig Equation (5)
  • 19. Open Middle: Build a Trig Equation (6)
  • 20. Open Middle: Build a Trig Equation (7)
  • 21. Open Middle: Build a Trig Equation (8)
  • 22. Basic Trig Graphing Open Middle Problem
  • 23. Basic Trig Graphing Open Middle Problem
  • 24. Important Trigonometric Limits

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7.

Trigonometric Identities

Illustrating and proving Trigonometric Identities

  • 1. Trigonometric Identities via Symmetry of the Unit Circle
  • 2. Another Popular Trig Identity
  • 3. Pythagorean Trigonometric Identity (1)
  • 4. Trig Identity via Areas: Dynamic Illustrator
  • 5. Trig ID Movie (II)
  • 6. Trig Identity via Areas (2): Dynamic Illustrator
  • 7. Trig ID Movie (III)
  • 8. Cosine and Secant Functions (Special Property)
  • 9. Cosine Identity
  • 10. Sine Identity
  • 11. Tangent Identity
  • 12. Trig Identity Shown Graphically
  • 13. Trigonometry Angle Sum Identities
  • 14. Double and Half Angle Identities
  • 15. Double Angle Trig Identity: Proof via Equal Areas
  • 16. Trig Identity (4) - Geometric Investigation
  • 17. Trig ID: Geometric Investigation
  • 18. Trig Identity (3) - Geometric Investigation
  • 19. Trigonometric identities: Part I
  • 20. Trigonometric identities: Part II
  • 21. Trigonometric identities: Part III
  • 22. Special Trigonometric Identities: Quick Exploration
  • 23. Tangent of a Difference: Trig Identity Puzzle + Proof!
  • 24. A Very Unusual Trig Identity
  • 25. Trig Identities from Similar Right Triangles (I)
  • 26. Proofs in Trigonometric Identities Practice : Scaffolded with Drag n Drop
  • 27. New Trig ID's from Similar Right Triangles (V2)
  • 28. New Trig IDs From Similar Right Triangles
  • 29. Trig Identities from Similar Right Triangles (II)
  • 30. Bizzare Trig Identity?
  • 31. Bizzare Trig Identity?
  • 32. Double Angle Identity Activity
  • 33. Copy of Visual Proof of ASin+BCos Identity
  • 34. Trig identities 1
  • 35. Adding sinusoidal waves (AI HL 1.13)

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8.

Inverse Trigonometric Functions

Defining and Graphing Inverse Trigonometric Functions Properties of Inverse Trigonometric Functions

  • 1. Inverse Trigonometric Functions
  • 2. Inverse Trig Functions: Intuitive Explorations
  • 3. Using Inverse Trig Functions to Express Angle Measures
  • 4. Evaluating Inverse Trig Functions of Special Ratios
  • 5. 4Q Quiz: Evaluating Inverse Trig Functions of Special Ratios
  • 6. 4Q Quiz: Using Inverse Trig Functions to Express Angle Measures
  • 7. Compositions of Trig & Inverse Trig Functions (1)
  • 8. Evaluating Compositions of Trig & Inverse Trig Functions (2)
  • 9. 4Q Quiz: Compositions of Trig & Inverse Trig Functions (1)
  • 10. Graphing Inverse Trig Functions

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9.

Trigonometric Equations and Inequalities

Solving Trigonometric Equations and Inequalities

  • 1. Solving Trigonometric Equations
  • 2. Principle of Solving Simple Trigonometric Equations
  • 3. Trigonometric Equations(SEE)

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10.

Solving General Triangles

Law of Sines & Law of Cosines

  • 1. Law of Cosines
  • 2. Euclid II 12 The Law Of Cosines Obtuse
  • 3. The Law of Cosines
  • 4. Law of Cosines: Discovery
  • 5. Proof Without Words: Hunger's Law of Cosine Dissection
  • 6. Law of Cosines (Circle Proof)
  • 7. Law of Sines
  • 8. Law of Sines (& Area)
  • 9. Law of Sines (Illustrated)
  • 10. Law of Sines: Intro via Areas
  • 11. Solving Triangles
  • 12. Solve Oblique Quick Quiz

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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 Dot and Cross Product
  • 10. 3D Vector Components: Dynamic Illustrator
  • 11. Battleship in the Coordinate Plane!
  • 12. Entering Vectors

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12.

Parametric Graphs


    Ce chapitre ne contient aucune ressource pour l'instant.

13.

Polar Coordinates

Defining Polar Coordinates Graphing Polar Functions


    Ce chapitre ne contient aucune ressource pour l'instant.

14.

Complex Numbers

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


    Ce chapitre ne contient aucune ressource pour l'instant.

15.

Applications


    Ce chapitre ne contient aucune ressource pour l'instant.

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