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Unit Circle and Sine Graph by Becky Angus

Unit Circle and Sine Graph by Becky Angus
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2015-01-03 04:32
CircleFunctionTrigonometryCoordinate GeometryGraphing
This example dynamically demonstrates the relationship between a point on the unit circle and the generated sine curve, visually showing the geometric meaning of the sine function. Core math concepts include the unit circle, trigonometric functions, sine function, and coordinate geometry. Construction highlights the use of GeoGebra commands and objects like Point, Rotate, Angle, Function, Segment, Circle, Vector, Sequence to rotate a point on the unit circle and plot its corresponding sine function, helping students understand the formation process of the sine wave. Suitable for high school students learning about trigonometric functions and the connection between function graphs.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Rotate(A, θ, B) → P
  3. Rotate(A, θ, B) → A'
  4. Angle(A, B, A') → α
  5. Rotate(A, θ, B) → A'_1
  6. Angle(A, B, A'_1) → β
  7. Function(sin(120° * x), 0, x(Q)) → f
  8. Segment(Q, (x(Q), 0)) → e
  9. Circle(B, A) → c
  10. Segment(B, P) → a
  11. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  12. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  13. Vector((0, 0), (x(Corner[2]), 0)) → z
  14. Sequence(Segment[(0.75 * i, 0), (0.75 * i, -0.025)], i, 1, 4) → list1
  15. Segment(P, (x(P), 0)) → b
  16. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  17. Sequence(Segment[(0, 0.5 * i - 1), (-0.025, 0.5 * i - 1)], i, 0, 4) → list2
  18. Sequence(Segment[(x(B), 0.5 * i - 1), (x(B) - 0.025, 0.5 * i - 1)], i, 0, 4) → list3
  19. Segment(P, Q) → d
  20. Sequence(Segment[B + (0.5 * i - 1, 0), B + (0.5 * i - 1, -0.025)], i, 0, 4) → list4
  21. Point(Ray[(0, 0), (-1, 0)]) → B_1
  22. Rotate(A_1, θ, B_1) → P_1
  23. Rotate(A_1, θ, B_1) → A'_2
  24. Rotate(A_1, θ, B_1) → A'_3
  25. Circle(B_1, A_1) → c_1
  26. Segment(B_1, P_1) → a_1

AI Drawing Prompt Reference

Draw a unit circle with a point moving along it. As the point moves, plot the corresponding sine function curve. Show the relationship between the point's position on the circle and its corresponding point on the sine wave, demonstrating the geometric meaning of the sine function dynamically. Include the unit circle, sine curve, points, line segments, and angles. Start with the point at the left side of the circle, moving along the circumference, connecting its vertical projection to the sine value.
The prompt above was compiled from the original drawing commands and is for reference only.