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Regions Bounded by Polar Curves

Regions Bounded by Polar Curves
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2017-09-05 00:22
FunctionTrigonometryCoordinate Geometry
In collections Multivariable Calculus
This example demonstrates how to use GeoGebra to draw polar curves and observe the regions bounded by these curves by adjusting parameters. Key mathematical concepts include polar coordinates, curve sketching, and area calculation. The construction uses commands like CurveCartesian, Textfield, and InputBox.

GeoGebra Commands & Parameters

  1. CurveCartesian((f(t) * cos(t)), (f(t) * sin(t)), t, α, β) → Cf
  2. Textfield(α) → InputBox1
  3. Textfield(β) → InputBox2
  4. CurveCartesian((g(t) * cos(t)), (g(t) * sin(t)), t, α, β) → Cg
  5. CurveCartesian((h(t) * cos(t)), (h(t) * sin(t)), t, α, β) → Ch
  6. CurveCartesian((g(t) * cos(t)), (g(t) * sin(t)), t, π, (3 * π / 2)) → d
  7. CurveCartesian((h(t) * cos(t)), (h(t) * sin(t)), t, π / 6, (5 * π / 6)) → e