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Sine Angle Addition

Sine Angle Addition
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2018-12-28 22:22
AngleFunctionTrigonometry
This example demonstrates the geometric meaning of sine angle addition. The core mathematical concepts involved are the sine function in trigonometry. By examining the commands in the construction summary, it can be seen that the example uses objects such as intersection, point, segment, and angle. Suitable for high school mathematics education and learning about the properties of the sine function.

GeoGebra Commands & Parameters

  1. Intersect(c, xAxis, 2) → B
  2. Point(c) → C
  3. Point(c) → D
  4. Intersect(xAxis, yAxis) → A
  5. Segment(A, B) → f
  6. Segment(A, C) → g
  7. Segment(A, D) → h
  8. Angle(B, A, C) → α
  9. Angle(C, A, D) → β
  10. If(a < 1, Segment[D, (x(D), y(D) - (y(D) * a))], Segment[D, (x(D), 0)]) → i
  11. Intersect(f, i) → E
  12. Angle(B, E, D) → γ
  13. OrthogonalLine(D, g) → j
  14. Intersect(j, g) → F
  15. If(1.5 < a < 2.5, Segment[D, (x(D) + ((a - 1.5) * (x(F) - x(D))), y(D) + ((a - 1.5) * (y(F) - y(D))))], a ≥ 2.5, Segment[D, F]) → k
  16. Angle(C, F, D) → δ
  17. If(3 < a < 4, Segment[F, (x(F), y(F) - (y(F) * (a - 3)))], a ≥ 4, Segment[F, (x(F), 0)]) → l
  18. Intersect(f, l) → G
  19. Angle(B, G, F) → ε
  20. If(4.5 < a < 5.5, Segment[F, (x(F) - ((x(F) - x(E)) * (a - 4.5)), y(F))], a ≥ 5.5, Segment[F, (x(E), y(F))]) → m
  21. Intersect(i, m) → H
  22. Angle(F, H, D) → ζ
  23. Angle(H, F, A) → η
  24. Angle(H, D, F) → θ

AI Drawing Prompt Reference

Draw a geometric demonstration of sine angle addition involving a coordinate system with x and y axes. Start by plotting intersection points B and constructing points C and D. Connect A to B, C, and D with line segments, labeling angles α and β. Then, draw line segment i based on parameter a, find intersection E with line f, and label angle γ. Next, draw a perpendicular line j to g, find intersection F, and based on a, draw segments k and l, finding intersection G with f and labeling angle ε. Finally, draw segment m based on a, find intersection H with i, and label angles ζ, η, and θ to illustrate the geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.