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极坐标与直角坐标比较

极坐标与直角坐标比较
几何画板及绘图内容加载中，请稍等……
2019-09-28 03:21
向量三角函数解析几何
本范例展示了极坐标系与直角坐标系中的点和图形的比较。核心数学概念包括坐标系、向量和三角函数。通过使用GeoGebra命令如Sequence、Point、Text等，可以动态地展示点在不同坐标系下的表示方式。适合高中数学教学和学习。

GeoGebra 命令及参数

  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