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Polar Area by Doug Kuhlmann

Polar Area by Doug Kuhlmann
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2015-06-20 18:27
FunctionTrigonometryCoordinate GeometryCalculus
This example demonstrates how to plot polar area graphs, visualizing the regions of sine and tangent functions in polar coordinates. It involves core math concepts like polar coordinate systems, area calculation, trigonometric properties, standard deviation, and addition. GeoGebra commands and objects used include Cartesian curve plotting, sequence generation, Zip, text fields, first/last extraction, summation, and integration. Suitable for high school and above students to understand the construction of polar graphs and the visualization of function area relationships.

GeoGebra Commands & Parameters

  1. CurveCartesian((r(θ) * cos(θ)), (r(θ) * sin(θ)), θ, 0, 6.283185307179586) → c
  2. Sequence(c(α + (i * Δθ)), i, 0, n) → ThetaPts
  3. Zip(CircleSector[(0, 0), C, D], C, First[ThetaPts, n], D, Last[ThetaPts, n]) → LSecs
  4. Textfield(r) → rOFtheta
  5. Textfield(α) → αEq
  6. Textfield(β) → βEq
  7. Last(ThetaPts, n) → Rpt
  8. First(ThetaPts, n) → Lpt
  9. Zip((Length[A]; Angle[B]), A, Rpt, B, Lpt) → Rtpts
  10. Zip(CircleSector[(0, 0), E, F], E, Rtpts, F, Last[ThetaPts, n]) → RSecs
  11. Sum(Sequence[((0.5 * r(α + (i * Δθ))^(2)) * Δθ), i, 0, n - 1]) → LSum
  12. Sum(Sequence[((0.5 * r(α + (i * Δθ))^(2)) * Δθ), i, 1, n]) → RSum
  13. Sequence(c(α + ((i - 1 / 2) * Δθ)), i, 1, n) → Midθpts
  14. Sum(Zip[((0.5 * R^(2)) * Δθ), R, Midθpts]) → MSum
  15. Zip((Length[A]; Angle[B]), A, Midθpts, B, First[ThetaPts, n]) → Mminus
  16. Zip((Length[A]; Angle[B]), A, Midθpts, B, Last[ThetaPts, n]) → Mplus
  17. Zip(CircleSector[(0, 0), E, F], E, Mminus, F, Mplus) → MSecs
  18. Integral(g, α, β) → Int