Polar Curve Plotter: Dynamic Input and Negative Radius Visualization

This GeoGebra example demonstrates how to plot polar curves of the form r = f(θ), with negative values of r displayed in a distinct color to highlight their geometric interpretation. It covers core concepts of polar coordinates, the relationship between radial distance and angle, trigonometric functions, and parametric representation. The construction uses input boxes (inputBox1, inputBox2, inputBox3) for users to define the function f(θ) and the angular range (minθ, maxθ), and employs the CurveCartesian command to convert the polar equation into a Cartesian parametric curve for plotting. Additional elements like Vector and Textfield are used to build an interactive interface. This resource is suitable for high school or early college students learning polar coordinates, function graphing, and parametric equations, as well as for teachers demonstrating how different polar equations (e.g., rose curves, spirals) change with parameters.