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Trigonometric Ratios Demo by MsPond

Trigonometric Ratios Demo by MsPond
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2019-04-09 02:02
AngleTrigonometryGeometric Construction
This example demonstrates the calculation and visualization of trigonometric ratios (sine, cosine, tangent) in right-angled triangles. It involves core math concepts like the definition of trigonometric functions, relationships between side lengths in right triangles, and angle measurement. Construction highlights include using GeoGebra commands such as Rotate, Angle, Segment, and Point to build right triangles and label relevant elements. Suitable for high school students learning trigonometric basics and geometric constructions.

GeoGebra Commands & Parameters

  1. Rotate(A, 90°, B) → C
  2. Angle(A, B, C) → α
  3. Segment(B, A) → b
  4. Segment(B, C) → g
  5. Point(g) → D
  6. Segment(D, B) → h
  7. Angle(B, D, A) → β
  8. Segment(D, A) → c
  9. Angle(D, A, B) → a
  10. Rotate(A_1, 90°, B_1) → C_1
  11. Angle(A_1, B_1, C_1) → α_1
  12. Segment(B_1, A_1) → b_1
  13. Segment(B_1, C_1) → g_1
  14. Point(g_1) → D_1
  15. Segment(D_1, B_1) → h_1
  16. Angle(B_1, D_1, A_1) → β_1
  17. Segment(D_1, A_1) → c_1
  18. Angle(D_1, A_1, B_1) → a_1
  19. Rotate(A_2, 90°, B_2) → C_2
  20. Angle(A_2, B_2, C_2) → α_2
  21. Segment(B_2, A_2) → b_2
  22. Segment(B_2, C_2) → g_2
  23. Point(g_2) → D_2
  24. Segment(D_2, B_2) → h_2
  25. Angle(B_2, D_2, A_2) → β_2
  26. Segment(D_2, A_2) → c_2
  27. Angle(D_2, A_2, B_2) → a_2
  28. Rotate(A_3, 90°, B_3) → C_3
  29. Angle(A_3, B_3, C_3) → α_3
  30. Segment(B_3, A_3) → b_3
  31. Segment(B_3, C_3) → g_3
  32. Point(g_3) → D_3
  33. Segment(D_3, B_3) → h_3
  34. Angle(B_3, D_3, A_3) → β_3
  35. Segment(D_3, A_3) → c_3
  36. Angle(D_3, A_3, B_3) → a_3

AI Drawing Prompt Reference

Draw a diagram demonstrating trigonometric ratios with three right-angled triangles. Each triangle should label the hypotenuse, opposite side, and adjacent side, along with the corresponding angles and trigonometric values. Start by drawing a right triangle, then rotate the hypotenuse 90 degrees to create a second triangle, and rotate again for a third. Label each triangle's angles α, β, a, and sides b, g, h, c, displaying the calculated trigonometric values.
The prompt above was compiled from the original drawing commands and is for reference only.