Polar and Rectangular Coordinates Conversion by Jamie Hansen

This interactive GeoGebra example demonstrates the conversion between polar coordinates (r, θ) and rectangular coordinates (x, y) for a point in the plane. It visually shows how the polar radius and angle relate to the Cartesian x and y components using trigonometric functions. The construction employs GeoGebra commands such as OrthogonalLine, Intersect, Segment, Point, Angle, and Midpoint to build the polar axis, the radius segment, the angle, and the perpendicular projections onto the x and y axes. Dynamic sliders or draggable points update the coordinates in real time, making the relationship clear. This resource is suitable for high school or introductory college students studying coordinate geometry, trigonometry, or precalculus, and serves as an effective teaching aid for demonstrating the equivalence and transformation between polar and rectangular coordinate systems.