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Golden ratio with trigonometric functions

Golden ratio with trigonometric functions
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2019-03-13 23:27
TriangleFunctionTrigonometryGeometric Construction
This example demonstrates the geometric manifestation of the golden ratio through triangles, highlighting the relationship between trigonometric functions and geometric shapes. Key concepts include the golden ratio, trigonometric functions, and their applications in geometry. Construction involves GeoGebra commands such as Intersect, Tangent, and Distance. Suitable for high school students or math enthusiasts to explore the interplay between geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(f, g, (0.6662394327302258, 0.7861513776105101)) → A
  2. Tangent(A, f) → h
  3. Tangent(A, g) → i
  4. Intersect(i, xAxis) → B
  5. Intersect(h, xAxis) → C
  6. Distance(A, C) → AC
  7. Distance(A, B) → AB

AI Drawing Prompt Reference

Draw a geometric figure demonstrating the golden ratio through trigonometric functions, involving two function graphs and their intersection point, tangent lines from the intersection point to the x-axis, and the distances between key points to highlight the relationship between trigonometric functions and geometric shapes.
The prompt above was compiled from the original drawing commands and is for reference only.