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Smallest and Largest Values (Part 1)

Smallest and Largest Values (Part 1)
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2022-06-02 22:04
TrigonometrySolid GeometryOptimization
In collections Open Middle: Interior and Exterior Angles of Triangles
This example demonstrates how to explore the smallest and largest values in hyperbolas, trigonometric functions, and solids using GeoGebra. Key mathematical concepts include hyperbolas, trigonometric functions, and solids. Using commands like Textfield, Intersect, Point, Line, Ray, Segment, Rotate, Angle, Polygon, etc., complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(a) → InputBox1
  2. Textfield(b) → InputBox2
  3. Textfield(c) → InputBox3
  4. Textfield(d) → InputBox4
  5. Textfield(f) → InputBox5
  6. Textfield(g) → InputBox6
  7. Textfield(h) → InputBox7
  8. Intersect(xAxis, yAxis) → A
  9. Point(xAxis) → C
  10. Line(A, C) → i
  11. Ray(C, A) → j
  12. Ray(C, B) → k
  13. Segment(B, A) → l
  14. Ray(D, E) → m
  15. Rotate(E, (((10 * d) + f) * π / 180), D) → E'
  16. Ray(D, E') → n
  17. Angle(E, D, E') → α
  18. Point(n) → F
  19. Rotate(D, (((10 * g) + h) * π / 180), F) → D'
  20. Ray(F, D') → p
  21. Angle(D, F, D') → β
  22. Intersect(m, p) → G
  23. Rotate(F, ((-((100 * a) + (10 * b) + c)) * π / 180), G) → F'
  24. Ray(G, F') → q
  25. Segment(F, G) → r
  26. Angle(F', G, F) → γ
  27. Polygon(F, D, G) → t1, g_1, f_1, d_1
  28. Polygon(A, B, C) → t2, b_1, a_1, c_1
  29. Mode(l1) → l2

AI Drawing Prompt Reference

Draw a hyperbola and a line i through points A and C. Construct rays j and k from point C, and a segment l from point B to point A. Then rotate points E and D to generate new points E' and D', and construct angles α, β, and γ. Finally, use these points to construct two triangles t1 and t2, and a segment r.
The prompt above was compiled from the original drawing commands and is for reference only.