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Demonstration of Sine Ratio Concept

Demonstration of Sine Ratio Concept
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2020-03-02 03:47
AngleFunctionTrigonometryGeometric ConstructionSlider Animation
This example dynamically demonstrates the concept of the sine ratio in right triangles, ① showing how the ratio of the opposite side to the hypotenuse changes as the angle θ varies; ② involving core mathematical concepts: sine function, trigonometry, angles, right triangles; ③ construction highlights: using commands like Point, Rotate, Ray, Angle, Segment, Polygon, Midpoint, Corner, and objects such as θ, X, O, B' for calculation and display; ④ suitable for high school mathematics teaching, used to understand the definition of trigonometric functions and their practical applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → X
  2. Rotate(X, θ, O) → B'
  3. Ray(O, B') → f
  4. Point(f) → A
  5. Angle(X, O, B') → α
  6. Ray(O, X) → g
  7. Point(f) → A_1
  8. Point(f) → A_2
  9. Point(f) → A_3
  10. Segment(O, A_1) → h_1
  11. Segment(O, A_2) → h_2
  12. Segment(O, A_3) → h_3
  13. Segment(A_1, B_1) → o_1
  14. Segment(A_2, B_2) → o_2
  15. Polygon(O, A, B) → p_1, i, j, k
  16. Segment(A_3, B_3) → o_3
  17. Angle(A_1, B_1, O) → β_1
  18. Angle(A_2, B_2, O) → β_2
  19. Angle(A_3, B_3, O) → β_3
  20. Segment(A, B) → o
  21. Angle(A, B, O) → ε
  22. Segment(O, A) → h
  23. Segment(O, B) → a
  24. Midpoint(o_1) → M_1
  25. Midpoint(o_2) → M_2
  26. Midpoint(o_3) → M_3
  27. Segment(O, B_1) → a_1
  28. Segment(O, B_2) → a_2
  29. Segment(O, B_3) → a_3
  30. Corner(1, 1) → C
  31. Midpoint(o) → M

AI Drawing Prompt Reference

Draw a right triangle with one leg aligned with the x-axis and the right angle at the origin. Use a slider to control angle θ, rotate one leg to form the other leg, and draw the hypotenuse. Mark several points on the hypotenuse, draw segments from these points to the right angle, and calculate the angles between these segments and the hypotenuse. Also, calculate and display the lengths of these segments, as well as the angle between the hypotenuse and the x-axis. Finally, draw the perpendicular bisector of the hypotenuse and display all calculated angles and segment lengths to demonstrate the sine ratio concept.
The prompt above was compiled from the original drawing commands and is for reference only.