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Polar and Rectangular Coordinates by Arthur Lee

Polar and Rectangular Coordinates by Arthur Lee
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2014-10-27 17:44
VectorFunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Conics And Polar Coordinates Polar Coordinates
This example demonstrates the conversion between polar and rectangular coordinates on different grids. It involves core math concepts like coordinate transformation, vectors, sequences, and geometric constructions. GeoGebra commands like Sequence, Point, Text, Vector, and conditional statements (If) are used to plot points, display vectors, and show coordinates. Suitable for high school and above, focusing on coordinate systems and geometric representations.

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, "P(" + (Length[P_{pol}]) + ", " + (arg(P_{pol})) + ")", "P(" + (Length[P_{rec}]) + ", " + (arg(P_{rec})) + ")") → textPolar
  19. If(fixPolar, "P(" + (x(P_{pol})) + ", " + (y(P_{pol})) + ")", "P(" + (x(P_{rec})) + ", " + (y(P_{rec})) + ")") → textRect

AI Drawing Prompt Reference

Draw a graph showing the conversion between polar and rectangular coordinates. The graph includes a circle centered at the origin with radius R. Four directions are marked on the circle: 90 degrees, 180 degrees, 0 degrees, and 270 degrees, with text labels. There are radius line segments from the origin, and text labels for each quadrant. The construction order is to draw the circle first, then add direction markers, then draw radius segments, and finally add quadrant text.
The prompt above was compiled from the original drawing commands and is for reference only.