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Tangent Function Demonstration by Patrick Kennedy

Tangent Function Demonstration by Patrick Kennedy
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2018-01-31 22:36
FunctionTrigonometryGeometric Construction
This example dynamically demonstrates the variation of the tangent value (opposite over adjacent) of angle θ in a right triangle. It involves core math concepts: trigonometric functions, right triangles, side-angle relationships. Construction highlights include using GeoGebra commands like Ray, Rotate, Angle, Point, Segment, OrthogonalLine, Intersect, Line, Polygon to build and visualize the dynamic behavior. Suitable for high school students learning the definition and properties of the tangent function.

GeoGebra Commands & Parameters

  1. Ray(A, B_1) → a
  2. Rotate(B_1, θ, A) → G
  3. Ray(A, C_1) → b
  4. Angle(B_1, A, C_1) → α_1
  5. Point(a) → F
  6. Segment(A, F) → c
  7. Segment(F, B_1) → d
  8. Point(c) → B
  9. OrthogonalLine(B, c) → e
  10. Point(d) → D
  11. OrthogonalLine(D, d) → g
  12. Intersect(e, b) → C
  13. Intersect(g, b) → E
  14. Point(g) → I
  15. Line(I, a) → h
  16. OrthogonalLine(A, a) → i
  17. Intersect(h, i) → J
  18. Intersect(g, h) → K
  19. Segment(D, I) → f
  20. Segment(A, J) → j
  21. Segment(J, I) → AD
  22. Segment(A, B) → AB
  23. Segment(C, B) → BC
  24. Segment(B, D) → k
  25. Segment(E, D) → DE
  26. Segment(A, E) → l
  27. Polygon(A, B, C) → veelhoek1, c_1, a_1, b_1
  28. Polygon(A, D, E) → veelhoek2, e_1, a_2, d_1
  29. Angle(C, B, A) → β_1
  30. Angle(E, D, A) → γ
  31. Angle(B, A, C) → β

AI Drawing Prompt Reference

Draw a right triangle ABC with angle A as the right angle, point B to the right of A, and point C below A. Then draw a ray AG from point A with angle θ. Next, draw rays a and b from point A, forming angle α₁ with ray AG. Take point F on ray a and draw line segment c connecting AF and FB. Take point B on line segment c and draw a line e perpendicular to c through B. Take point D on line segment d and draw a line g perpendicular to d through D. Line e intersects ray b at point C, and line g intersects ray b at point E. Draw line h from point I to ray a, and draw a line i perpendicular to ray a through A. Line h intersects line i at point J, and line g intersects line h at point K. Draw line segment DI, AJ, JI, AB, BC, BD, DE, and AE.
The prompt above was compiled from the original drawing commands and is for reference only.