Trigonometry

Tim Brzezinski, 9. 8. 2017

Obsah

  1. Prerequisites
    1. Perpendicular Lines: Quick Intro
    2. Complementary Meaning?
    3. Supplementary Angles (Quick Exploration)
    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)
  2. Standard Position & Vocab
    1. Angles in Standard Position
    2. Angle Orientations (Standard Position)
    3. Coterminal Angles Action!!!
  3. 6 Trig Functions; Quadrant Logic
    1. The 6 Trigonometric Functions: Quick Illustrator
    2. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
    3. Evaluating Trig Functions Given a Point on the Terminal Ray
    4. Quiz: Quadrant Logic (Trig)
    5. Trig Quadrant Logic (2)
    6. Trig Ratio Possibilities (Hints)
    7. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    8. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
  4. Right Triangle Trig (Q1)
    1. Right Triangle Generator for Right Triangle Trigonometry
    2. Right Triangles: Identifying Sides WRT Acute Angles
    3. Identifying Trig Ratios: Quick Formative Assessment
    4. Finding Exact Trig Ratios: Quiz Question Generator
    5. Right Triangle Trigonometry: Intro
    6. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
    7. Trig Ratio Estimations (Right Triangle Context)
    8. Trig Ratio Estimations (Quiz: V1)
    9. Right Triangle Solver: Formative Assessment
    10. Right Triangle Trig: Solving for Sides
    11. Right Triangle Trig: Solving for Sides (2)
    12. Finding Acute Angles of Right Triangles
    13. Quiz: Expressing Angles Using Inverse Trigonometric Function
    14. What "CO" in COsine Means
  5. Radians, Arc Length, Sector Area
    1. What is a Radian?
    2. Radian Illustrator
    3. 1 Radian: Clear Definition
    4. Constructing Angles Given Radian Measure
    5. Quiz: Sketching Angles in Standard Position
    6. TRUE MEANING of π
    7. Circumference = ? (Animation)
    8. Circumference = ? (Animation II)
    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?
    20. Who's Going Faster?
  6. Trig FNS 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. Trig Reference Circle: Choose Your Own Radius
    7. Trig Reference Circle (2): Choose Your Own Radius
    8. Rads and Revs: Quick Conceptual Insight
    9. Trig Circle: Coordinates of Special Angle Values
    10. Special Angles in Standard Position: Intro (V2)
    11. Special Angles in Standard Position: Intro (V3)
    12. Quiz 1: Trigonometric Functions of Special Angles
    13. Quiz 2: Trigonometric Functions of Special Angles
  7. Graphing and Writing Trig Functions & Equations
    1. Parent Sine and Cosine Functions
    2. Sine and Cosine Graphing Template
    3. Sine and Cosine π-friendly Graphing Template
    4. Sine Spaghetti (by Steve Phelps)
    5. Cosine Spaghetti
    6. Sine Function Anatomy and Exploration
    7. Unit Circle to Sine and Cosine Functions
    8. Tangent Function Exploration
    9. Cotangent Function Exploration
    10. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
    11. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
    12. Sine & Cosine Period Action (1)!
    13. Periodic Function Action!
    14. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
    15. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
    16. Basic Trig Graphing Open Middle Problem
    17. Open Middle: Graphing Trig Functions Exercise
    18. Graphing Sine & Cosine Functions (Amp, Period, Vertical Shift Changes Only)
    19. Graphing Sine and Cosine Functions (Includes All Transformations)
    20. Modeling with Trigonometric Functions
    21. Open Middle: Trigonometric Equation (1)
    22. Open Middle: Trigonometric Equation (2)
    23. Open Middle: Creating Trig EQ's Exercise Set
    24. Transforming the Sine Function (All Transformations)
    25. Graphing Sine & Cosine Functions (I)
    26. Graphing Sine & Cosine Functions (II)
  8. Inverse Trig Functions
    1. Using Inverse Trig Functions to Express Angle Measures
    2. Creating Inverse Sine and Inverse Cosine Functions
    3. Inverse Trig Functions: Intuitive Explorations
    4. Evaluating Inverse Trig Functions of Special Ratios
    5. Compositions of Trig & Inverse Trig Functions (1)
    6. Evaluating Compositions of Trig & Inverse Trig Functions (2)
  9. Proving Trig ID's
    1. New Trig IDs From Similar Right Triangles
    2. New Trig ID's from Similar Right Triangles (V2)
    3. Another Popular Trig Identity
    4. Trig Identity via Areas: Dynamic Illustrator
    5. Trig Identity via Areas (2): Dynamic Illustrator
    6. Sine & Cosine of a Sum: Discovery
    7. Tangent of a Sum: Discovery
    8. Cotangent of a Sum: Discovery
    9. Trig ID: Geometric Investigation
    10. Trig ID (2) - Geometric Investigation
    11. Trig Identity (3) - Geometric Investigation
    12. Trig Identity (4) - Geometric Investigation
    13. Double Angle Trig Identity: Proof via Equal Areas
    14. Trig Identity Shown Graphically
  10. Advanced Topics
    1. Special Trigonometric Identities: Quick Exploration
    2. Exploring Sines: Another Key Triangle Relationship
    3. Law of Sines: Intro via Areas
    4. Law of Sines (& Area)
    5. Interesting Triangles Phenomenon
    6. SSA Theorem?
    7. Ambiguous Case (SSA) Illustrator: All Cases
    8. Open Middle: Ambiguous Case Setups
    9. Law of Cosines: Discovery
    10. Law of Cosines: Open Middle Problem (V1)
    11. Open Middle Problem: Law of Cosines (V2)
  11. Bearings (Applications)
    1. Bearing Illustrator (1)
    2. Bearing: Dynamic Illustration
    3. Bearing Illustrator (2)
    4. Bearings: Dynamic Illustrator
    5. Bearings: NEWS Components
    6. Setting Up Bearings
    7. Open Middle: Bearings Exercise
  12. 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
  13. Dot Product
    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.

Prerequisites

  • 1. Perpendicular Lines: Quick Intro
  • 2. Complementary Meaning?
  • 3. Supplementary Angles (Quick Exploration)
  • 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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2.

Standard Position & Vocab

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

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6 Trig Functions; Quadrant Logic

  • 1. The 6 Trigonometric Functions: Quick Illustrator
  • 2. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
  • 3. Evaluating Trig Functions Given a Point on the Terminal Ray
  • 4. Quiz: Quadrant Logic (Trig)
  • 5. Trig Quadrant Logic (2)
  • 6. Trig Ratio Possibilities (Hints)
  • 7. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
  • 8. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)

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4.

Right Triangle Trig (Q1)

  • 1. Right Triangle Generator for Right Triangle Trigonometry
  • 2. Right Triangles: Identifying Sides WRT Acute Angles
  • 3. Identifying Trig Ratios: Quick Formative Assessment
  • 4. Finding Exact Trig Ratios: Quiz Question Generator
  • 5. Right Triangle Trigonometry: Intro
  • 6. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
  • 7. Trig Ratio Estimations (Right Triangle Context)
  • 8. Trig Ratio Estimations (Quiz: V1)
  • 9. Right Triangle Solver: Formative Assessment
  • 10. Right Triangle Trig: Solving for Sides
  • 11. Right Triangle Trig: Solving for Sides (2)
  • 12. Finding Acute Angles of Right Triangles
  • 13. Quiz: Expressing Angles Using Inverse Trigonometric Function
  • 14. What "CO" in COsine Means

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5.

Radians, Arc Length, Sector Area

  • 1. What is a Radian?
  • 2. Radian Illustrator
  • 3. 1 Radian: Clear Definition
  • 4. Constructing Angles Given Radian Measure
  • 5. Quiz: Sketching Angles in Standard Position
  • 6. TRUE MEANING of π
  • 7. Circumference = ? (Animation)
  • 8. Circumference = ? (Animation II)
  • 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?
  • 20. Who's Going Faster?

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6.

Trig FNS 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. Trig Reference Circle: Choose Your Own Radius
  • 7. Trig Reference Circle (2): Choose Your Own Radius
  • 8. Rads and Revs: Quick Conceptual Insight
  • 9. Trig Circle: Coordinates of Special Angle Values
  • 10. Special Angles in Standard Position: Intro (V2)
  • 11. Special Angles in Standard Position: Intro (V3)
  • 12. Quiz 1: Trigonometric Functions of Special Angles
  • 13. Quiz 2: Trigonometric Functions of Special Angles

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7.

Graphing and Writing Trig Functions & Equations

  • 1. Parent Sine and Cosine Functions
  • 2. Sine and Cosine Graphing Template
  • 3. Sine and Cosine π-friendly Graphing Template
  • 4. Sine Spaghetti (by Steve Phelps)
  • 5. Cosine Spaghetti
  • 6. Sine Function Anatomy and Exploration
  • 7. Unit Circle to Sine and Cosine Functions
  • 8. Tangent Function Exploration
  • 9. Cotangent Function Exploration
  • 10. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
  • 11. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
  • 12. Sine & Cosine Period Action (1)!
  • 13. Periodic Function Action!
  • 14. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
  • 15. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
  • 16. Basic Trig Graphing Open Middle Problem
  • 17. Open Middle: Graphing Trig Functions Exercise
  • 18. Graphing Sine & Cosine Functions (Amp, Period, Vertical Shift Changes Only)
  • 19. Graphing Sine and Cosine Functions (Includes All Transformations)
  • 20. Modeling with Trigonometric Functions
  • 21. Open Middle: Trigonometric Equation (1)
  • 22. Open Middle: Trigonometric Equation (2)
  • 23. Open Middle: Creating Trig EQ's Exercise Set
  • 24. Transforming the Sine Function (All Transformations)
  • 25. Graphing Sine & Cosine Functions (I)
  • 26. Graphing Sine & Cosine Functions (II)

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8.

Inverse Trig Functions

  • 1. Using Inverse Trig Functions to Express Angle Measures
  • 2. Creating Inverse Sine and Inverse Cosine Functions
  • 3. Inverse Trig Functions: Intuitive Explorations
  • 4. Evaluating Inverse Trig Functions of Special Ratios
  • 5. Compositions of Trig & Inverse Trig Functions (1)
  • 6. Evaluating Compositions of Trig & Inverse Trig Functions (2)

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Proving Trig ID's

  • 1. New Trig IDs From Similar Right Triangles
  • 2. New Trig ID's from Similar Right Triangles (V2)
  • 3. Another Popular Trig Identity
  • 4. Trig Identity via Areas: Dynamic Illustrator
  • 5. Trig Identity via Areas (2): Dynamic Illustrator
  • 6. Sine & Cosine of a Sum: Discovery
  • 7. Tangent of a Sum: Discovery
  • 8. Cotangent of a Sum: Discovery
  • 9. Trig ID: Geometric Investigation
  • 10. Trig ID (2) - Geometric Investigation
  • 11. Trig Identity (3) - Geometric Investigation
  • 12. Trig Identity (4) - Geometric Investigation
  • 13. Double Angle Trig Identity: Proof via Equal Areas
  • 14. Trig Identity Shown Graphically

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10.

Advanced Topics

  • 1. Special Trigonometric Identities: Quick Exploration
  • 2. Exploring Sines: Another Key Triangle Relationship
  • 3. Law of Sines: Intro via Areas
  • 4. Law of Sines (& Area)
  • 5. Interesting Triangles Phenomenon
  • 6. SSA Theorem?
  • 7. Ambiguous Case (SSA) Illustrator: All Cases
  • 8. Open Middle: Ambiguous Case Setups
  • 9. Law of Cosines: Discovery
  • 10. Law of Cosines: Open Middle Problem (V1)
  • 11. Open Middle Problem: Law of Cosines (V2)

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11.

Bearings (Applications)

  • 1. Bearing Illustrator (1)
  • 2. Bearing: Dynamic Illustration
  • 3. Bearing Illustrator (2)
  • 4. Bearings: Dynamic Illustrator
  • 5. Bearings: NEWS Components
  • 6. Setting Up Bearings
  • 7. Open Middle: Bearings Exercise

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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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Dot Product

  • 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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Informace