Polar and Rectangular Coordinates Conversion by Tosha Kelsey

This interactive GeoGebra example demonstrates the conversion between polar coordinates (r, α) and rectangular coordinates (x, y) for a point in the plane. It visually shows how the same point can be represented in two different coordinate systems, highlighting the roles of cosine and sine in projecting the polar radius onto the x- and y-axes. The construction uses GeoGebra commands such as OrthogonalLine, Intersect, Segment, Point, Angle, and Textfield to build the coordinate axes, point A, perpendicular lines b and c, segment a, point D, angle α, distance r, coordinate components xa and ya, along with dynamic text labels and an input box for user interaction. Users can modify the input values or drag the point to see real-time updates of both coordinate representations. This resource is suitable for high school or early college students learning analytic geometry and coordinate transformations, and serves as an effective teaching tool for instructors to illustrate the geometric meaning and conversion formulas between polar and rectangular coordinates.