CCSS High School: Functions (Trigonometric Functions)

Tim Brzezinski, mark vasicek, May 6, 2018

[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
    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
    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. Coterminal Angles: Question Generator
    9. Defining Trigonometric Ratios
    10. Unit Circle and Sine Graph
    11. Unit Circle and Tangent Graph
    12. Unit Circle and Cosine Graph
  3. HSF.TF.A.3
    1. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
    2. Evaluating Trig Functions Given a Point on the Terminal Ray
    3. Quiz: Quadrant Logic (Trig)
    4. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    5. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
    6. Right Triangle Trigonometry: Intro
    7. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
    8. Right Triangle Trig: Solving for Sides (2)
    9. Quiz: Expressing Angles Using Inverse Trigonometric Function
    10. Trig Ratio Estimations (Right Triangle Context)
    11. Trig Ratio Estimations (Quiz: V1)
    12. Trig Ratio Estimations (Quiz: V2)
    13. Isosceles Right Triangle: Quick Investigation
    14. Special Right Triangle (I)
    15. Another Special Right Triangle (Guided Discovery)
    16. Special Right Triangle (II)
    17. 30-60-90 Triangle
    18. Quiz: Special Right Triangles
    19. Trig Function Values (30 Degrees)
    20. Animation 148
    21. Trig Function Values (45 Degrees)
    22. Animation 146
    23. Trig Function Values (60 Degrees)
    24. Animation 147
    25. Special Angles in Standard Position: Intro (V1)
    26. Special Angles in Standard Position: Intro (V2)
    27. Special Angles in Standard Position: Intro (V2) - Part 2
    28. Animation 177
    29. Animation 178
    30. Special Angles in Standard Position: Intro (V3)
    31. Animation 182
    32. Quiz 1: Trigonometric Functions of Special Angles
    33. Quiz 2: Trigonometric Functions of Special Angles
  4. HSF.TF.A.4
    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
    1. Sine & Cosine Period Action (1)!
    2. Animation 190
    3. Animation 191
    4. Sine & Cosine Period Action (2)!
    5. Tangent Period Action (1)!
    6. Tangent Period Action (2)!
    7. Animation 192
    8. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
    9. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
    10. Graphing Sine & Cosine Functions (II)
    11. Graphing Sine & Cosine Functions (I)
    12. Transformations of a Sinusoid
    13. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
    14. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
    15. Sine Function Modeling (y = a sin(x) + d) Quiz
    16. Cosine Function Modeling (y = a cos(x) + d) Quiz
    17. Modeling with Trigonometric Functions
    18. Sine & Cosine Function Modeling: Finding Correct Parameters
    19. Ferris Wheel Action!!!
  6. HSF.TF.B.6
    1. Inverse Relations: Graphs
    2. Sine Function Domain Restriction Options?
    3. Cosine Function Domain Restriction Options?
    4. Tangent Function Domain Restriction Options?
  7. HSF.TF.B.7
    1. Ferris Wheel (1): Modeling with Trigonometric Functions
    2. Ferris Wheel (2): Modeling with Trigonometric Functions
  8. HSF.TF.C.8
    1. Pythagorean Trigonometric Identity (1)
    2. Trig ID Movie (II)
    3. Trig ID Movie (III)
  9. HSF.TF.C.9
    1. Sine & Cosine of a Sum: Discovery
    2. Tangent of a Sum: Discovery
    3. Tangent of a Difference: Trig Identity Puzzle + Proof!
    4. Cotangent of a Sum: Discovery
    5. Bizzare Trig Identity?
    6. Animation 105
    7. 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

  • 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

  • 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. Coterminal Angles: Question Generator
  • 9. Defining Trigonometric Ratios
  • 10. Unit Circle and Sine Graph
  • 11. Unit Circle and Tangent Graph
  • 12. 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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3.

HSF.TF.A.3

  • 1. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
  • 2. Evaluating Trig Functions Given a Point on the Terminal Ray
  • 3. Quiz: Quadrant Logic (Trig)
  • 4. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
  • 5. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
  • 6. Right Triangle Trigonometry: Intro
  • 7. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
  • 8. Right Triangle Trig: Solving for Sides (2)
  • 9. Quiz: Expressing Angles Using Inverse Trigonometric Function
  • 10. Trig Ratio Estimations (Right Triangle Context)
  • 11. Trig Ratio Estimations (Quiz: V1)
  • 12. Trig Ratio Estimations (Quiz: V2)
  • 13. Isosceles Right Triangle: Quick Investigation
  • 14. Special Right Triangle (I)
  • 15. Another Special Right Triangle (Guided Discovery)
  • 16. Special Right Triangle (II)
  • 17. 30-60-90 Triangle
  • 18. Quiz: Special Right Triangles
  • 19. Trig Function Values (30 Degrees)
  • 20. Animation 148
  • 21. Trig Function Values (45 Degrees)
  • 22. Animation 146
  • 23. Trig Function Values (60 Degrees)
  • 24. Animation 147
  • 25. Special Angles in Standard Position: Intro (V1)
  • 26. Special Angles in Standard Position: Intro (V2)
  • 27. Special Angles in Standard Position: Intro (V2) - Part 2
  • 28. Animation 177
  • 29. Animation 178
  • 30. Special Angles in Standard Position: Intro (V3)
  • 31. Animation 182
  • 32. Quiz 1: Trigonometric Functions of Special Angles
  • 33. 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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4.

HSF.TF.A.4

  • 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

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

HSF.TF.B.6

  • 1. Inverse Relations: Graphs
  • 2. Sine Function Domain Restriction Options?
  • 3. Cosine Function Domain Restriction Options?
  • 4. Tangent Function Domain Restriction Options?

6.1.

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6.2.

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6.3.

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6.4.

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7.

HSF.TF.B.7

  • 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

  • 1. Pythagorean Trigonometric Identity (1)
  • 2. Trig ID Movie (II)
  • 3. Trig ID Movie (III)

8.1.

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8.2.

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8.3.

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9.

HSF.TF.C.9

  • 1. Sine & Cosine of a Sum: Discovery
  • 2. Tangent of a Sum: Discovery
  • 3. Tangent of a Difference: Trig Identity Puzzle + Proof!
  • 4. Cotangent of a Sum: Discovery
  • 5. Bizzare Trig Identity?
  • 6. Animation 105
  • 7. 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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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