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Polar Coordinates

Polar Coordinates
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2020-04-17 15:37
VectorFunctionCoordinate Geometry
This example demonstrates points and curves in the polar coordinate system, which uses distance and angle to represent points. Using GeoGebra commands like Vector, CurveCartesian, Line, and Angle, the example constructs points and curves in the polar coordinate system. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector((0, 0), ((r * cos(θ)), (r * sin(θ)))) → rvec
  2. CurveCartesian((cos(t) * f(t)), (sin(t) * f(t)), t, 0, (2 * π)) → r1
  3. Line(P, (0, 0)) → AngleLine
  4. Vector((0, 0), (100, 0)) → Xvec
  5. Angle(Xvec, Vector[If[r > 0, rvec, ((-x(P)), (-y(P)))]]) → PolarAngle
  6. Angle(Vector[((-x(P)), (-y(P)))], Vector[P]) → RNegAngle

AI Drawing Prompt Reference

Draw a vector from the origin representing distance and angle in polar coordinates, a line from the origin, and two angles between the x-axis and the vector, one for the vector itself and one for its negative. Finally, plot a curve defined by a function f(t) in polar coordinates to show points and curves in the system.
The prompt above was compiled from the original drawing commands and is for reference only.