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Trigonometric Sequence and 3D Shape Demonstration

Trigonometric Sequence and 3D Shape Demonstration
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2019-01-12 03:20
VectorTrigonometrySequenceCoordinate GeometrySolid Geometry
This example demonstrates the dynamic changes and graphical construction of trigonometric sequences in 3D space; involves core math concepts like trigonometric functions, sequences, 3D geometry, and vector operations; construction highlights: using commands like Point, Vector, Sequence, Zip to create points, vectors, and sequences, combined with Segment, Textfield for graphical interface; suitable for high school and above mathematics teaching, for understanding the integration of functions, sequences, and spatial geometry.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_1
  2. Vector(A_1, B_1) → u
  3. Textfield(f) → inputBox1
  4. Vector(A_1, B_2) → v
  5. Vector(B_2, A_2) → w
  6. Vector(x_*, C_1) → z
  7. Segment(D_1, X) → j
  8. Sequence(t, t, (-6 * π / B), (6 * π / B), (2 * π / B)) → nums
  9. Zip((0, sol1 + k), k, nums) → SourcePtsMD
  10. Zip((0, sol2 + k), k, nums) → SourcePts2MD
  11. Zip((sol1 + k, f(sol1 + k)), k, nums) → TrigGraphpts
  12. Zip((sol2 + k, f(sol2 + k)), k, nums) → TrigGraphPts2
  13. Zip(Vector[(0, sol1 + k), (2, f(sol1 + k))], k, nums) → TrigMD
  14. Zip(Vector[(0, sol2 + k), (2, f(sol2 + k))], k, nums) → TrigMDSup

AI Drawing Prompt Reference

Create a 3D space demonstration of a trigonometric sequence, including a point A on the x-axis, vector u from A to B1, vector v from A to B2, vector w from B2 to A2, and vector z from x-axis point x_* to C1. Use these vectors and points to construct a series of points forming the trigonometric graph. Dynamically adjust parameters to show the changes in the trigonometric sequence.
The prompt above was compiled from the original drawing commands and is for reference only.