CCSS High School: Functions (Trigonometric Functions)

Tim Brzezinski, Ronan Downes, Mar 10, 2020

[b][color=#1551b5]This GeoGebra Book contains discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of concepts related to trigonometric functions. [/color] [/b]

Table of Contents

  1. HSF.TF.A.1: Working with radians
    1. 1 Radian: Clear Definition
    2. Animation 69
    3. Radian Illustrator
    4. Movie: Radians to Revs
    5. DEG to RAD and RAD to DEG Illustrator
    6. DEG to RAD and RAD to DEG: Question Generator
  2. HSF.TF.A.2: Angles in standard position, coterminal angles, trigonometric ratios
    1. Angles in Standard Position
    2. Animation 176
    3. Angle Orientations (Standard Position)
    4. Animation 180
    5. Animation 181
    6. Coterminal Angles Action!!!
    7. Animation 183
    8. Quiz: Sketching Angles in Standard Position
    9. Coterminal Angles: Question Generator
    10. Defining Trigonometric Ratios
    11. Unit Circle and Sine Graph
    12. Unit Circle and Tangent Graph
    13. Unit Circle and Cosine Graph
  3. HSF.TF.A.3: Trigonometric functions of special angles (multiples of pi/6 & pi/4)
    1. Right Triangle Generator for Right Triangle Trigonometry
    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. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    7. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
    8. Right Triangle Trigonometry: Intro
    9. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
    10. Right Triangle Solver: Formative Assessment
    11. Right Triangle Trig: Solving for Sides (2)
    12. Quiz: Expressing Angles Using Inverse Trigonometric Function
    13. Trig Ratio Estimations (Right Triangle Context)
    14. Trig Ratio Estimations (Quiz: V1)
    15. Trig Ratio Estimations (Quiz: V2)
    16. Isosceles Right Triangle: Quick Investigation
    17. Special Right Triangle (I)
    18. Another Special Right Triangle (Guided Discovery)
    19. Special Right Triangle (II)
    20. 30-60-90 Triangle
    21. Special Right Triangles: Basic Questions
    22. Quiz: Special Right Triangles
    23. Trig Function Values (30 Degrees)
    24. Animation 148
    25. Trig Function Values (45 Degrees)
    26. Animation 146
    27. Trig Function Values (60 Degrees)
    28. Animation 147
    29. Special Angles in Standard Position: Intro (V1)
    30. Special Angles in Standard Position: Intro (V2)
    31. Special Angles in Standard Position: Intro (V2) - Part 2
    32. Animation 177
    33. Animation 178
    34. Special Angles in Standard Position: Intro (V3)
    35. Animation 182
    36. Quiz 1: Trigonometric Functions of Special Angles
    37. Quiz 2: Trigonometric Functions of Special Angles
  4. HSF.TF.A.4: Which trig functions are even? odd?
    1. Sine and Cosecant Functions (Special Property)
    2. Sine Identity
    3. Animation 150
    4. Cosine and Secant Functions (Special Property)
    5. Cosine Identity
    6. Animation 149
    7. Tangent and Cotangent Functions (Special Property)
    8. Animation 145
    9. Tangent Identity
    10. Animation 151
  5. HSF.TF.B.5: Graphing and writing trigonometric functions
    1. Unit Circle to Sine and Cosine Functions
    2. Sine & Cosine Period Action (1)!
    3. Animation 190
    4. Animation 191
    5. Sine & Cosine Period Action (2)!
    6. Tangent Function Exploration
    7. Tangent Period Action (1)!
    8. Tangent Period Action (2)!
    9. Animation 192
    10. Cotangent Function Exploration
    11. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
    12. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
    13. Transforming the Sine Function (All Transformations)
    14. Graphing Sine & Cosine Functions (II)
    15. Graphing Sine & Cosine Functions (I)
    16. Transformations of a Sinusoid
    17. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
    18. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
    19. Sine Function Modeling (y = a sin(x) + d) Quiz
    20. Cosine Function Modeling (y = a cos(x) + d) Quiz
    21. Modeling with Trigonometric Functions
    22. Sine & Cosine Function Modeling: Finding Correct Parameters
    23. Ferris Wheel Action!!!
  6. HSF.TF.B.6: Inverse trigonometric functions
    1. Inverse Relations: Graphs
    2. Sine Function Domain Restriction Options?
    3. Cosine Function Domain Restriction Options?
    4. Tangent Function Domain Restriction Options?
    5. Inverse Trig Functions: Intuitive Explorations
  7. HSF.TF.B.7: Solving trigonometric equations and modeling
    1. Ferris Wheel (1): Modeling with Trigonometric Functions
    2. Ferris Wheel (2): Modeling with Trigonometric Functions
  8. HSF.TF.C.8: Proving trigonometric identities
    1. New Trig IDs From Similar Right Triangles
    2. New Trig ID's from Similar Right Triangles (V2)
    3. Pythagorean Trigonometric Identity (1)
    4. Trig ID Movie (II)
    5. Trig ID Movie (III)
  9. HSF.TF.C.9: Proving advanced trigonometric identities
    1. Sine & Cosine of a Sum: Discovery
    2. Trig ID: Geometric Investigation
    3. Tangent of a Sum: Discovery
    4. Tangent of a Difference: Trig Identity Puzzle + Proof!
    5. Cotangent of a Sum: Discovery
    6. Bizzare Trig Identity?
    7. Animation 105
    8. sin(75) & cos(75) activity
  10. Links to Other CCSS High School: Functions Resources
    1. Functions Resources
  11. *Additional: Links to CCSS High School: Geometry Resources
    1. Geometry Resources

1.

HSF.TF.A.1: Working with radians

  • 1. 1 Radian: Clear Definition
  • 2. Animation 69
  • 3. Radian Illustrator
  • 4. Movie: Radians to Revs
  • 5. DEG to RAD and RAD to DEG Illustrator
  • 6. DEG to RAD and RAD to DEG: Question Generator

1.1.

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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

HSF.TF.A.2: Angles in standard position, coterminal angles, trigonometric ratios

  • 1. Angles in Standard Position
  • 2. Animation 176
  • 3. Angle Orientations (Standard Position)
  • 4. Animation 180
  • 5. Animation 181
  • 6. Coterminal Angles Action!!!
  • 7. Animation 183
  • 8. Quiz: Sketching Angles in Standard Position
  • 9. Coterminal Angles: Question Generator
  • 10. Defining Trigonometric Ratios
  • 11. Unit Circle and Sine Graph
  • 12. Unit Circle and Tangent Graph
  • 13. Unit Circle and Cosine Graph

2.1.

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2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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3.

HSF.TF.A.3: Trigonometric functions of special angles (multiples of pi/6 & pi/4)

  • 1. Right Triangle Generator for Right Triangle Trigonometry
  • 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. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
  • 7. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
  • 8. Right Triangle Trigonometry: Intro
  • 9. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
  • 10. Right Triangle Solver: Formative Assessment
  • 11. Right Triangle Trig: Solving for Sides (2)
  • 12. Quiz: Expressing Angles Using Inverse Trigonometric Function
  • 13. Trig Ratio Estimations (Right Triangle Context)
  • 14. Trig Ratio Estimations (Quiz: V1)
  • 15. Trig Ratio Estimations (Quiz: V2)
  • 16. Isosceles Right Triangle: Quick Investigation
  • 17. Special Right Triangle (I)
  • 18. Another Special Right Triangle (Guided Discovery)
  • 19. Special Right Triangle (II)
  • 20. 30-60-90 Triangle
  • 21. Special Right Triangles: Basic Questions
  • 22. Quiz: Special Right Triangles
  • 23. Trig Function Values (30 Degrees)
  • 24. Animation 148
  • 25. Trig Function Values (45 Degrees)
  • 26. Animation 146
  • 27. Trig Function Values (60 Degrees)
  • 28. Animation 147
  • 29. Special Angles in Standard Position: Intro (V1)
  • 30. Special Angles in Standard Position: Intro (V2)
  • 31. Special Angles in Standard Position: Intro (V2) - Part 2
  • 32. Animation 177
  • 33. Animation 178
  • 34. Special Angles in Standard Position: Intro (V3)
  • 35. Animation 182
  • 36. Quiz 1: Trigonometric Functions of Special Angles
  • 37. Quiz 2: Trigonometric Functions of Special Angles

3.1.

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3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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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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3.22.

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3.23.

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3.24.

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3.25.

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3.26.

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3.27.

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3.28.

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3.29.

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3.30.

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3.31.

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3.32.

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3.33.

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3.34.

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3.35.

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3.36.

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3.37.

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4.

HSF.TF.A.4: Which trig functions are even? odd?

  • 1. Sine and Cosecant Functions (Special Property)
  • 2. Sine Identity
  • 3. Animation 150
  • 4. Cosine and Secant Functions (Special Property)
  • 5. Cosine Identity
  • 6. Animation 149
  • 7. Tangent and Cotangent Functions (Special Property)
  • 8. Animation 145
  • 9. Tangent Identity
  • 10. Animation 151

4.1.

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4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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5.

HSF.TF.B.5: Graphing and writing trigonometric functions

  • 1. Unit Circle to Sine and Cosine Functions
  • 2. Sine & Cosine Period Action (1)!
  • 3. Animation 190
  • 4. Animation 191
  • 5. Sine & Cosine Period Action (2)!
  • 6. Tangent Function Exploration
  • 7. Tangent Period Action (1)!
  • 8. Tangent Period Action (2)!
  • 9. Animation 192
  • 10. Cotangent Function Exploration
  • 11. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
  • 12. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
  • 13. Transforming the Sine Function (All Transformations)
  • 14. Graphing Sine & Cosine Functions (II)
  • 15. Graphing Sine & Cosine Functions (I)
  • 16. Transformations of a Sinusoid
  • 17. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
  • 18. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
  • 19. Sine Function Modeling (y = a sin(x) + d) Quiz
  • 20. Cosine Function Modeling (y = a cos(x) + d) Quiz
  • 21. Modeling with Trigonometric Functions
  • 22. Sine & Cosine Function Modeling: Finding Correct Parameters
  • 23. Ferris Wheel Action!!!

5.1.

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5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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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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5.15.

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5.16.

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5.17.

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5.18.

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5.19.

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5.20.

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5.21.

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5.22.

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5.23.

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6.

HSF.TF.B.6: Inverse trigonometric functions

  • 1. Inverse Relations: Graphs
  • 2. Sine Function Domain Restriction Options?
  • 3. Cosine Function Domain Restriction Options?
  • 4. Tangent Function Domain Restriction Options?
  • 5. Inverse Trig Functions: Intuitive Explorations

6.1.

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6.2.

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6.3.

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6.4.

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6.5.

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7.

HSF.TF.B.7: Solving trigonometric equations and modeling

  • 1. Ferris Wheel (1): Modeling with Trigonometric Functions
  • 2. Ferris Wheel (2): Modeling with Trigonometric Functions

7.1.

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7.2.

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8.

HSF.TF.C.8: Proving trigonometric identities

  • 1. New Trig IDs From Similar Right Triangles
  • 2. New Trig ID's from Similar Right Triangles (V2)
  • 3. Pythagorean Trigonometric Identity (1)
  • 4. Trig ID Movie (II)
  • 5. Trig ID Movie (III)

8.1.

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8.2.

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8.3.

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8.4.

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8.5.

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9.

HSF.TF.C.9: Proving advanced trigonometric identities

  • 1. Sine & Cosine of a Sum: Discovery
  • 2. Trig ID: Geometric Investigation
  • 3. Tangent of a Sum: Discovery
  • 4. Tangent of a Difference: Trig Identity Puzzle + Proof!
  • 5. Cotangent of a Sum: Discovery
  • 6. Bizzare Trig Identity?
  • 7. Animation 105
  • 8. sin(75) & cos(75) activity

9.1.

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9.2.

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9.3.

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9.4.

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9.5.

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9.6.

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9.7.

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9.8.

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10.

Links to Other CCSS High School: Functions Resources

  • 1. Functions Resources

10.1.

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11.

*Additional: Links to CCSS High School: Geometry Resources

  • 1. Geometry Resources

11.1.

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Information