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Helix View - Unit Tangent & Normal Vectors

Helix View - Unit Tangent & Normal Vectors
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2017-09-05 22:20
VectorTrigonometryCoordinate Geometry
This example demonstrates the unit tangent and normal vectors of a helix. Key mathematical concepts include vectors, trigonometry, and coordinate geometry. Using GeoGebra commands such as CurveCartesian and Vector, the helix and its tangent and normal vectors are constructed. Suitable for high school mathematics education and learning about helix properties.

GeoGebra Commands & Parameters

  1. CurveCartesian((2 * cos(t)), (2 * sin(t)), t, t, 0, (10 * π)) → c
  2. Vector(((2 * cos(t)), (2 * sin(t)), t)) → v
  3. Vector(((2 * cos(t)), (2 * sin(t)), t), ((2 * cos(t)) + ((-((2 * sin(t))))) / sqrt(5), (2 * sin(t)) + ((2 * cos(t))) / sqrt(5), t + 1 / sqrt(5))) → w
  4. Vector(((2 * cos(t)), (2 * sin(t)), t), ((2 * cos(t)) + (-0.5 * cos(t)), (2 * sin(t)) + (-0.5 * sin(t)), t)) → u