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Sine Riding on Sine: Vector Translation and Polygon Animation

Sine Riding on Sine: Vector Translation and Polygon Animation
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2016-12-10 20:24
PolygonVectorTrigonometryTransformationGraphing
This example demonstrates the superposition of sine waves or vector translation effects. Core concepts involve trigonometric functions, vector arithmetic, and polygon construction. It is constructed using GeoGebra commands like Vector, Translate, and Polygon, utilizing points A, B, C, D and functions f, g for dynamic visualization. Suitable for high school or college mathematics education to intuitively understand function transformations and vector synthesis, aiding classroom demonstrations or student exploration.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(C, D) → v
  3. Translate(f, Vector[(a * u)]) → f_4
  4. Polygon((0, 1.1), (12.566370614359176, 1.1), (12.566370614359176, -1.1), (0, -1.1), (0, 1.1)) → poly1, b, c, d, e, h
  5. Translate(poly1, Vector[(-3 * v)]) → poly1'
  6. Translate(poly1, Vector[(-6 * v)]) → poly1'_1
  7. Translate(g, Vector[(a * u)]) → g_1
  8. Translate(p, Vector[(a * u)]) → p_1