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Parametric Curves in Space

Parametric Curves in Space
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2019-06-05 03:05
VectorCoordinate GeometryParametric Equation
This example demonstrates parametric curves in space, involving concepts of parametric equations, vectors, and coordinate geometry. Using commands like CurveCartesian and Vector, you can construct and explore these curves. Suitable for university calculus courses.

GeoGebra Commands & Parameters

  1. CurveCartesian((((4 + sin((20 * t))) * cos(t)), ((4 + sin((20 * t))) * sin(t)), cos((20 * t))), t, (-π), t_{tmax}) → q
  2. CurveCartesian((sin((3 * t)) * cos(t)), (sin((3 * t)) * sin(t)), t, t, (-π), t_{tmax}) → r
  3. CurveCartesian((cos(t), sin(t), sin((2 * t))), t, (-π), t_{tmax}) → p
  4. CurveCartesian((cos(t), sin(t), t), t, (-π), t_{tmax}) → h
  5. Vector(q(t_{tmax})) → v_{q}
  6. Vector(r(t_{tmax})) → v_{r}
  7. Vector(p(t_{tmax})) → v_{p}
  8. Vector(h(t_{tmax})) → v_{h}