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Unit Tangent and Unit Normal Vectors

Unit Tangent and Unit Normal Vectors
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2017-10-18 00:52
VectorCoordinate GeometryGeometric Construction
This example demonstrates the concepts of unit tangent and unit normal vectors. Core mathematical concepts include vectors and the tangents of curves. Using GeoGebra commands such as Vector, CurveCartesian, and Point, the tangent and normal vectors of a curve can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector((r_x(t), r_y(t))) → r
  2. CurveCartesian(b, sin(b), b, -500, 500) → myCurve
  3. Vector((x(r), y(r)), (1 / sqrt(1 + cos(t)^(2)) + x(r), cos(t) / sqrt(1 + cos(t)^(2)) + y(r))) → T
  4. Point(T) → AnglePoint1
  5. Vector((x(r), y(r)), (T'_x(t) / sqrt(T'_x(t)^(2) + T'_y(t)^(2)) + x(r), T'_y(t) / sqrt(T'_x(t)^(2) + T'_y(t)^(2)) + y(r))) → N
  6. Point(N) → AnglePoint3
  7. Point(T) → AnglePoint2
  8. Angle(AnglePoint1, AnglePoint2, AnglePoint3) → α
  9. Vector((x(r), y(r)), (T'_x(t) + x(r), T'_y(t) + y(r))) → T'
  10. Vector((x(r), y(r)), (r''_x(t) + x(r), r''_y(t) + y(r))) → a
  11. Vector((x(r), y(r)), (r'_x(t) + x(r), r'_y(t) + y(r))) → v

AI Drawing Prompt Reference

Draw a sine curve and its unit tangent and normal vectors. First, draw the curve y=sin(x). Then, calculate and draw the unit tangent vector at any point on the curve. Next, calculate and draw the unit normal vector at that point. Finally, mark the starting and ending points of these vectors and calculate the angle between them.
The prompt above was compiled from the original drawing commands and is for reference only.