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Compare Polar and Rectangular Coordinates

Compare Polar and Rectangular Coordinates
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2019-09-28 03:21
VectorTrigonometryCoordinate Geometry
This example demonstrates the comparison of points and figures in polar and rectangular coordinate systems. Key mathematical concepts include coordinate systems, vectors, and trigonometric functions. Using GeoGebra commands such as Sequence, Point, and Text, dynamic representations of points in different coordinate systems are shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[((r * cos(theta)), (r * sin(theta))), theta, 0°, 359°, SelectedElement[listAngle]], r, 0, R) → listPoint
  2. Point(listPoint) → P_{pol}
  3. Sequence(Circle[(0, 0), r], r, 1, R) → listCircle
  4. Text("90°", (-0.3, R + 0.5)) → text2
  5. Vector((R + 1, 0)) → u
  6. Text("180°", ((-R) - 1.8, -0.2)) → text3
  7. Text("0°", (R + 1.2, -0.2)) → text1
  8. Text("270°", (-0.5, (-R) - 1.2)) → text4
  9. Sequence(Text[r, (r - 0.2, -0.7)], r, 1, R) → listTextAxis
  10. SelectedElement(listAngle) → angle
  11. Sequence(Segment[(0, 0), ((R * cos(theta)), (R * sin(theta)))], theta, 0°, 360°, angle) → listRadiusThin
  12. SelectedIndex(listAngle) → angleIndex
  13. Sequence(Text[((theta / π * 180))°, (((R + 0.5) * cos(theta)), ((R + 0.5) * sin(theta)))], theta, If[angleIndex ≥ 3, angle, 10°], 89°, If[angleIndex ≥ 3, angle, 10°]) → listTextQ1
  14. Sequence(Text[((theta / π * 180))°, (((R + 0.4) * cos(theta)) - 1, ((R + 0.4) * sin(theta)))], theta, 90° + If[angleIndex ≥ 3, angle, 10°], 179°, If[angleIndex ≥ 3, angle, 10°]) → listTextQ2
  15. Sequence(Text[((theta / π * 180))°, (((R + 0.4) * cos(theta)) - 1, ((R + 0.4) * sin(theta)) - 0.6)], theta, 180° + If[angleIndex ≥ 3, angle, 10°], 269°, If[angleIndex ≥ 3, angle, 10°]) → listTextQ3
  16. Sequence(Text[((theta / π * 180))°, (((R + 0.4) * cos(theta)), ((R + 0.4) * sin(theta)) - 0.6)], theta, 270° + If[angleIndex ≥ 3, angle, 10°], 359°, If[angleIndex ≥ 3, angle, 10°]) → listTextQ4
  17. Sequence(Segment[(0, 0), ((R * cos(theta)), (R * sin(theta)))], theta, 0°, 360°, If[angleIndex ≥ 3, angle, 10°]) → listRadiusThick
  18. If(fixPolar, "(" + (Length[P_{pol}]) + ", " + (arg(P_{pol})) + ")", "(" + (Length[P_{rec}]) + ", " + (arg(P_{rec})) + ")") → textPolar
  19. If(fixPolar, "(" + (x(P_{pol})) + ", " + (y(P_{pol})) + ")", "(" + (x(P_{rec})) + ", " + (y(P_{rec})) + ")") → textRect