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Cal. 4 Lab 1

Cal. 4 Lab 1
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2020-01-13 01:01
VectorTrigonometryCalculusDerivativeParametric Equation
This example demonstrates the relationship between 3D vectors and derivatives. It uses vector and parametric equations to show how to calculate tangents. Key mathematical concepts include vectors, derivatives, and trigonometric functions. GeoGebra commands used include CurveCartesian, Tangent, and Vector. Suitable for university calculus courses.

GeoGebra Commands & Parameters

  1. CurveCartesian(tan(t^(1 / 2)), cos(t), tan(t^(t)), t, (-3 * π), (3 * π)) → a
  2. Tangent(P, a) → T
  3. Vector(P, P + a'(b) / Length[a'(b)]) → U
  4. Vector(P, P + a'(b)) → T_{v}

AI Drawing Prompt Reference

Draw a 3D curve defined by parametric equations: x(t) = tan(√t), y(t) = cos(t), z(t) = tan(t^t). Then, draw a tangent line at a specific point on the curve and calculate the direction vector and unit direction vector of the tangent.
The prompt above was compiled from the original drawing commands and is for reference only.