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Sine Addition Formula by Malin Christersson

Sine Addition Formula by Malin Christersson
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2014-02-18 03:50
AngleFunctionTrigonometry
Change the angles to see the cases in all four quadrants. This example demonstrates the sine addition formula, involving core mathematical concepts such as trigonometry and the unit circle. Through operations like rotation and constructing segments and angles, the sine addition formula can be visually understood. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Rotate(B, β, A) → B'
  4. Segment(B', A) → a_2
  5. Rotate(B', α, A) → B''
  6. OrthogonalLine(B'', xAxis) → j
  7. OrthogonalLine(B'', a_2) → d
  8. Intersect(d, a_2) → C
  9. OrthogonalLine(C, yAxis) → m
  10. Intersect(m, j) → E
  11. Circle(A, B) → c_2
  12. Angle(B, A, B') → γ
  13. Angle(B', A, B'') → δ
  14. Polygon(A, C, B'') → poly1, b'', a_1, c_1
  15. Angle(B'', C, A) → ε
  16. OrthogonalLine(C, xAxis) → f
  17. OrthogonalLine(B'', yAxis) → g
  18. Intersect(f, g) → D
  19. Angle(D, C, B'') → ζ
  20. Angle(E, C, B'') → η
  21. Angle(D, C, B'') → θ
  22. Angle(E, C, B'') → ι
  23. Segment(D, B'') → e
  24. Segment(E, C) → h
  25. Midpoint(B'', C) → F
  26. Midpoint(C, A) → G
  27. Vector(C', C) → u
  28. Vector(C, D) → v
  29. Vector(E, B'') → w
  30. Vector(A, P) → z

AI Drawing Prompt Reference

Draw a unit circle with center A and point B on the positive x-axis. Rotate point B by angles β and α to get points B' and B''. Draw perpendicular lines from B'' to the x-axis and line a_2, intersecting at point C. Draw perpendicular lines from C to the y-axis and x-axis, intersecting at points E and D. Connect the points to form triangles and angles, illustrating the sine addition formula.
The prompt above was compiled from the original drawing commands and is for reference only.