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Sine Wave on Cone

Sine Wave on Cone
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2022-04-20 11:57
TrigonometryCoordinate GeometrySolid Geometry
In collections Sine Wave on Surfaces
This example demonstrates a sine wave projected on a cone. It involves core concepts of trigonometry and coordinate geometry. Using GeoGebra commands such as Intersect, CurveCartesian, and Surface, one can construct a sine wave on a cone. Suitable for high school mathematics education, particularly in trigonometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → B
  2. CurveCartesian(((a * (1 + cos((n * t)))) * cos(t)), ((a * (1 + cos((n * t)))) * sin(t)), (c * (1 + cos((n * t)))), t, 0, (2 * π)) → f
  3. Surface(((a * u) * cos(v)), ((a * u) * sin(v)), (c * u), u, 0, π, v, 0, (2 * π)) → b

AI Drawing Prompt Reference

Draw a cone and a sine wave with a period of 2π on its surface. First, find the intersection of the x-axis and z-axis to serve as the cone's vertex. Then, use parametric equations to draw a sine wave that wraps around the cone's surface with a period of 2π. Finally, use parametric equations to draw the surface of the cone.
The prompt above was compiled from the original drawing commands and is for reference only.