Use the Ferris-wheel diagram at angle \(θ\) to state the normalized coordinates, signed vertical displacement from the center, and rider height in terms of \(R\) and \(H\).

Circular motion begins with the normalized point whose horizontal and vertical components are cosine and sine. Scaling by the radius turns those components into physical displacements, while adding the center's height converts signed vertical displacement into height above the ground. Keeping displacement and absolute height separate prevents a missing vertical shift.