Trigonometry

michael

Trigonometry applets and Dynamic interactions to understanding the concepts

차례

  1. Unit Circle/ Laws
    1. The Unit Circle
    2. Unit Circle - Identifying Coordinates for Important Angles
    3. Unit Circle
    4. Unwrapping a Circle
    5. Unwrapping the Unit Circle
    6. Sine an Cosine Components
    7. law of cosines (proof)
    8. law of sines (proof)
    9. Law of sines-ambiguous case
  2. Preliminary Content
    1. Perpendicular Lines: Quick Intro
    2. Complementary Angles Meaning
    3. Supplementary Angles Meaning
    4. Isosceles Triangle (Quick Construction Technique) V1
    5. Equilateral Triangle Construction (Dynamic Illustration)
    6. Proof Without Words
    7. Proof Without Words
    8. Practice: Pythagorean Theorem (1)
    9. Quiz: Pythagorean Theorem (2A)
    10. Quiz: Pythagorean Theorem (2B)
    11. Simplifying Radicals (I)
    12. Simplifying Radicals (II)
    13. Triangle Angle Sum Theorem (V4)
    14. Animation 171
    15. Isosceles Right Triangle: Quick Investigation
    16. Another Special Right Triangle (Guided Discovery)
    17. Special Right Triangle (II)
    18. Vertical Angles Exploration (1)
    19. Naming Angle Positions
    20. Transversal Intersects Parallel Lines
    21. Corresponding Angles: Quick Investigation
    22. Alternate Interior Angles: Quick Investigation
    23. Alternate Exterior Angles: Quick Investigation
    24. Same-Side-Interior Angles: Quick Investigation
    25. Same-Side-Exterior Angles: Quick Investigation
    26. Similar Figures: Dynamic Illustration
    27. AA Similarity Theorem
    28. SSS ~ Theorem (V2)
  3. Angles in Standard Position (and Related Vocabulary)
    1. Angles in Standard Position
    2. Angle Orientations (Standard Position)
    3. Coterminal Angles Action!!!
  4. The 6 Trigonometric Ratios; Right Triangle Trigonometry; Applications
    1. Right Triangles: Identifying Sides WRT Acute Angles
    2. Identifying Trig Ratios: Quick Formative Assessment
    3. Finding Exact Trig Ratios: Quiz Question Generator
    4. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
    5. Evaluating Trig Functions Given a Point on the Terminal Ray
    6. Quiz: Quadrant Logic (Trig)
    7. Trig Quadrant Logic (2)
    8. Trig Ratio Possibilities (Hints)
    9. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    10. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
    11. Right Triangle Generator for Right Triangle Trigonometry
    12. Right Triangle Trigonometry: Intro
    13. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
    14. Trig Ratio Estimations (Right Triangle Context)
    15. Trig Ratio Estimations (Quiz: V1)
    16. Right Triangle Solver: Formative Assessment
    17. Right Triangle Trig: Solving for Sides
    18. Right Triangle Trig: Solving for Sides (2)
    19. Using Inverse Trig Functions to Find Acute Angles of Right Triangles
    20. Quiz: Expressing Angles Using Inverse Trigonometric Function
    21. What "CO" in COsine Means
  5. Trigonometric Functions of Special Angles
    1. Trig Function Values (30 Degrees)
    2. Trig Function Values (45 Degrees)
    3. Trig Function Values (60 Degrees)
    4. Special Right Triangles: Basic Questions
    5. Quiz: Special Right Triangles
    6. Special Angles in Standard Position: Intro (V2)
    7. Special Angles in Standard Position: Intro (V3)
    8. Quiz 1: Trigonometric Functions of Special Angles
    9. Quiz 2: Trigonometric Functions of Special Angles
  6. Introduction to Radians; Arc Length and Area of a Sector
    1. Circle vs. Sphere
    2. Circle Terminology
    3. TRUE MEANING of π
    4. Circumference = ? (Animation)
    5. Circumference = ? (Animation II)
    6. 1 Radian: Clear Definition
    7. Radian Illustrator
    8. Quiz: Sketching Angles in Standard Position
    9. DEG to RAD and RAD to DEG Illustrator
    10. DEG to RAD and RAD to DEG: Question Generator
    11. Arc length: Quick Investigation
    12. Parallelogram: Area
    13. Triangle Area Action!!! (V2)
    14. Circle Area (By Peeling!)
    15. Arc Length and Area of a Sector (V1)
    16. Arc Length and Area of a Sector (V2)
    17. Area of a Sector
    18. Angular to Linear: Without Words
    19. YOUR Linear Speed?
  7. Graphing and Writing Trigonometric Functions
    1. Unit Circle to Sine and Cosine Functions
    2. Tangent Function Exploration
    3. Cotangent Function Exploration
    4. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
    5. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
    6. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
    7. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
    8. Periodic Function Action!
    9. Transforming the Sine Function (All Transformations)
    10. Sine & Cosine Period Action (1)!
    11. Graphing Sine & Cosine Functions (I)
    12. Graphing Sine & Cosine Functions (II)
    13. Modeling with Trigonometric Functions
    14. Inverse Trig Functions: Intuitive Explorations
  8. Proving Trig Identities
    1. New Trig IDs From Similar Right Triangles
    2. New Trig ID's from Similar Right Triangles (V2)
    3. Trig Identity via Areas: Dynamic Illustrator
    4. Trig Identity via Areas (2): Dynamic Illustrator
    5. Trig ID: Geometric Investigation
  9. Advanced Topics
    1. Special Trigonometric Identities: Quick Exploration
    2. Law of Sines (& Area)
    3. SSA Theorem?
    4. Ambiguous Case (SSA) Illustrator: All Cases
    5. Law of Cosines: Discovery
    6. Law of Cosines: Open Middle Problem (V1)
    7. Open Middle Problem: Law of Cosines (V2)
  10. Bearings (Applications)
    1. Bearing Illustrator (1)
    2. Bearing: Dynamic Illustration
    3. Bearing Illustrator (2)
    4. Bearings: Dynamic Illustrator
  11. Vectors
    1. Vectors: Magnitude & Direction (I)
    2. Scaling Vectors
    3. Vector Addition
    4. Quiz: Adding Vectors Geometrically
    5. Vector Subtraction
    6. Dot Product Insight
    7. Orthogonality Illustrated
    8. Dot Product: Basic Synthesis Questions
    9. Vector Projections (1)
    10. Quality Info?
    11. Vector Magnitude from Components
    12. Magnitude and Direction (Intro)
    13. Pac Man: Vector Components
  12. Dot Product Discovery Lesson
    1. Mystery Scalar Exploration (Part 1)
    2. Mystery Scalar Exploration (Part 1)
    3. Mystery Scalar Exploration (Part 3)
    4. Mystery Scalar Exploration (Part 4)
    5. Mystery Scalar Exploration (Part 5)
    6. Mystery Scalar Exploration (Part 6)
    7. Mystery Scalar Exploration (Part 7)
    8. Mystery Scalar Exploration (Part 8)
    9. Mystery Scalar Exploration (Part 9)

1.

Unit Circle/ Laws

Applets for connection between unit circle and graphs. Also, Law of cosines and sines with the ambiguous case

  • 1. The Unit Circle
  • 2. Unit Circle - Identifying Coordinates for Important Angles
  • 3. Unit Circle
  • 4. Unwrapping a Circle
  • 5. Unwrapping the Unit Circle
  • 6. Sine an Cosine Components
  • 7. law of cosines (proof)
  • 8. law of sines (proof)
  • 9. Law of sines-ambiguous case

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2.

Preliminary Content

  • 1. Perpendicular Lines: Quick Intro
  • 2. Complementary Angles Meaning
  • 3. Supplementary Angles Meaning
  • 4. Isosceles Triangle (Quick Construction Technique) V1
  • 5. Equilateral Triangle Construction (Dynamic Illustration)
  • 6. Proof Without Words
  • 7. Proof Without Words
  • 8. Practice: Pythagorean Theorem (1)
  • 9. Quiz: Pythagorean Theorem (2A)
  • 10. Quiz: Pythagorean Theorem (2B)
  • 11. Simplifying Radicals (I)
  • 12. Simplifying Radicals (II)
  • 13. Triangle Angle Sum Theorem (V4)
  • 14. Animation 171
  • 15. Isosceles Right Triangle: Quick Investigation
  • 16. Another Special Right Triangle (Guided Discovery)
  • 17. Special Right Triangle (II)
  • 18. Vertical Angles Exploration (1)
  • 19. Naming Angle Positions
  • 20. Transversal Intersects Parallel Lines
  • 21. Corresponding Angles: Quick Investigation
  • 22. Alternate Interior Angles: Quick Investigation
  • 23. Alternate Exterior Angles: Quick Investigation
  • 24. Same-Side-Interior Angles: Quick Investigation
  • 25. Same-Side-Exterior Angles: Quick Investigation
  • 26. Similar Figures: Dynamic Illustration
  • 27. AA Similarity Theorem
  • 28. SSS ~ Theorem (V2)

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3.

Angles in Standard Position (and Related Vocabulary)

  • 1. Angles in Standard Position
  • 2. Angle Orientations (Standard Position)
  • 3. Coterminal Angles Action!!!

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4.

The 6 Trigonometric Ratios; Right Triangle Trigonometry; Applications

  • 1. Right Triangles: Identifying Sides WRT Acute Angles
  • 2. Identifying Trig Ratios: Quick Formative Assessment
  • 3. Finding Exact Trig Ratios: Quiz Question Generator
  • 4. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
  • 5. Evaluating Trig Functions Given a Point on the Terminal Ray
  • 6. Quiz: Quadrant Logic (Trig)
  • 7. Trig Quadrant Logic (2)
  • 8. Trig Ratio Possibilities (Hints)
  • 9. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
  • 10. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
  • 11. Right Triangle Generator for Right Triangle Trigonometry
  • 12. Right Triangle Trigonometry: Intro
  • 13. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
  • 14. Trig Ratio Estimations (Right Triangle Context)
  • 15. Trig Ratio Estimations (Quiz: V1)
  • 16. Right Triangle Solver: Formative Assessment
  • 17. Right Triangle Trig: Solving for Sides
  • 18. Right Triangle Trig: Solving for Sides (2)
  • 19. Using Inverse Trig Functions to Find Acute Angles of Right Triangles
  • 20. Quiz: Expressing Angles Using Inverse Trigonometric Function
  • 21. What "CO" in COsine Means

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5.

Trigonometric Functions of Special Angles

  • 1. Trig Function Values (30 Degrees)
  • 2. Trig Function Values (45 Degrees)
  • 3. Trig Function Values (60 Degrees)
  • 4. Special Right Triangles: Basic Questions
  • 5. Quiz: Special Right Triangles
  • 6. Special Angles in Standard Position: Intro (V2)
  • 7. Special Angles in Standard Position: Intro (V3)
  • 8. Quiz 1: Trigonometric Functions of Special Angles
  • 9. Quiz 2: Trigonometric Functions of Special Angles

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6.

Introduction to Radians; Arc Length and Area of a Sector

  • 1. Circle vs. Sphere
  • 2. Circle Terminology
  • 3. TRUE MEANING of π
  • 4. Circumference = ? (Animation)
  • 5. Circumference = ? (Animation II)
  • 6. 1 Radian: Clear Definition
  • 7. Radian Illustrator
  • 8. Quiz: Sketching Angles in Standard Position
  • 9. DEG to RAD and RAD to DEG Illustrator
  • 10. DEG to RAD and RAD to DEG: Question Generator
  • 11. Arc length: Quick Investigation
  • 12. Parallelogram: Area
  • 13. Triangle Area Action!!! (V2)
  • 14. Circle Area (By Peeling!)
  • 15. Arc Length and Area of a Sector (V1)
  • 16. Arc Length and Area of a Sector (V2)
  • 17. Area of a Sector
  • 18. Angular to Linear: Without Words
  • 19. YOUR Linear Speed?

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7.

Graphing and Writing Trigonometric Functions

  • 1. Unit Circle to Sine and Cosine Functions
  • 2. Tangent Function Exploration
  • 3. Cotangent Function Exploration
  • 4. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
  • 5. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
  • 6. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
  • 7. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
  • 8. Periodic Function Action!
  • 9. Transforming the Sine Function (All Transformations)
  • 10. Sine & Cosine Period Action (1)!
  • 11. Graphing Sine & Cosine Functions (I)
  • 12. Graphing Sine & Cosine Functions (II)
  • 13. Modeling with Trigonometric Functions
  • 14. Inverse Trig Functions: Intuitive Explorations

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8.

Proving Trig Identities

  • 1. New Trig IDs From Similar Right Triangles
  • 2. New Trig ID's from Similar Right Triangles (V2)
  • 3. Trig Identity via Areas: Dynamic Illustrator
  • 4. Trig Identity via Areas (2): Dynamic Illustrator
  • 5. Trig ID: Geometric Investigation

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Advanced Topics

  • 1. Special Trigonometric Identities: Quick Exploration
  • 2. Law of Sines (& Area)
  • 3. SSA Theorem?
  • 4. Ambiguous Case (SSA) Illustrator: All Cases
  • 5. Law of Cosines: Discovery
  • 6. Law of Cosines: Open Middle Problem (V1)
  • 7. Open Middle Problem: Law of Cosines (V2)

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Bearings (Applications)

  • 1. Bearing Illustrator (1)
  • 2. Bearing: Dynamic Illustration
  • 3. Bearing Illustrator (2)
  • 4. Bearings: Dynamic Illustrator

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Vectors

Applets about Vector Operations

  • 1. Vectors: Magnitude & Direction (I)
  • 2. Scaling Vectors
  • 3. Vector Addition
  • 4. Quiz: Adding Vectors Geometrically
  • 5. Vector Subtraction
  • 6. Dot Product Insight
  • 7. Orthogonality Illustrated
  • 8. Dot Product: Basic Synthesis Questions
  • 9. Vector Projections (1)
  • 10. Quality Info?
  • 11. Vector Magnitude from Components
  • 12. Magnitude and Direction (Intro)
  • 13. Pac Man: Vector Components

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12.

Dot Product Discovery Lesson

  • 1. Mystery Scalar Exploration (Part 1)
  • 2. Mystery Scalar Exploration (Part 1)
  • 3. Mystery Scalar Exploration (Part 3)
  • 4. Mystery Scalar Exploration (Part 4)
  • 5. Mystery Scalar Exploration (Part 5)
  • 6. Mystery Scalar Exploration (Part 6)
  • 7. Mystery Scalar Exploration (Part 7)
  • 8. Mystery Scalar Exploration (Part 8)
  • 9. Mystery Scalar Exploration (Part 9)

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정보