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Unit Circle and Trigonometric Functions by Brandon Perez

Unit Circle and Trigonometric Functions by Brandon Perez
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2015-07-06 23:50
CircleFunctionTrigonometryGeometric ConstructionSlider Animation
In collections The Unit Circle Begins
This example demonstrates the relationship between the unit circle and trigonometric functions (sine, cosine, tangent) by showing the correspondence between angles and function values through rotation. Key concepts include the unit circle, definition of trigonometric functions, angle rotation, and tangent line. Construction highlights the use of commands like Circle, Point, Segment, OrthogonalLine, Angle, Mirror, and Rotate. It is suitable for high school mathematics teaching, helping students understand the connection between trigonometric function graphs and the unit circle, as well as the application of geometric transformations in function definitions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → B
  4. Segment(A, B) → a
  5. OrthogonalLine(B, xAxis) → b
  6. Angle(xAxis, a) → Θ_1
  7. Intersect(c, a) → D,
  8. Point(c) → F
  9. Point(c) → G
  10. Mirror(H, yAxis) → H'
  11. Mirror(H', xAxis) → H''
  12. Mirror(H'', yAxis) → H'''
  13. Mirror(I, yAxis) → I'
  14. Mirror(I', xAxis) → I''
  15. Mirror(I'', yAxis) → I'''
  16. Mirror(J, yAxis) → J'
  17. Mirror(J', xAxis) → J''
  18. Mirror(J'', yAxis) → J'''
  19. Intersect(c, xAxis, 2) → E
  20. Rotate(E, Θ_2, A) → E'_1
  21. Angle(E, A, E'_1) → Θ
  22. Segment(A, E'_1) → d
  23. OrthogonalLine(E'_1, xAxis) → e
  24. Intersect(e, xAxis) → C
  25. Segment(E'_1, C) → f
  26. Segment(A, C) → g
  27. Segment(A, C) → h
  28. Intersect(c, yAxis, 2) → K
  29. Mirror(K, xAxis) → K'
  30. Intersect(c, xAxis, 1) → L
  31. Mirror(L, yAxis) → L'