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Example 3: Tangent Line to a Helix

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Published: 29 Sept 2025 › Updated: 29 Sept 2025Example 3: Tangent Line to a Helix

Example 3: Tangent Line to a Helix

In this video I show how to obtain the parametric equations of a line that is tangent to a given point on a helix, whose parametric equations are also given. I first convert the helix parametric equations to its vector equation form and then take the derivative. I then obtain the parametric equations of our tangent line by using our given point and the derivative as the parallel vector. I also graph this out in GeoGebra's amazing 3D graphing calculator, play around with it yourself! https://www.geogebra.org/3d/na9yk6pn

#math #helix #calculus #vectors #geogebra

5 Helix Tangent Line.jpeg

Timestamps

  • Example 3: Tangent line to a helix: 0:00
  • Converting parametric equations to vector equation of the helix and taking the derivative: 0:32
  • Obtaining parameter value at our given point on the helix: 1:10
  • Derivative at our point on the helix: 3:11
  • Recap on the parametric equations of a line: 4:03
  • Obtaining the parametric equations of our tangent line: 5:33
  • Graph of the tangent line to the helix, and input equations for GeoGebra: 8:25
  • Graphing in GeoGebra's 3D graphing calculator: 10:57

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