Ferris Wheel Functions

Algebra 2 · Axiom Academy

Ride one seat around a turning wheel, watch its height rise and fall, and meet the wave that launches trigonometry. Going in circles, going up and down A Ferris wheel turns at a steady, unremarkable pace — but the seat you are sitting in does something more interesting. It climbs, crests, sinks to the bottom, and climbs again, over and over. That rising-and-falling height is the single most important shape in trigonometry, and you can watch it appear. Watch one rider go around at a constant speed. A level line tracks the rider's height above the ground , and on the right that height is plotted against the angle turned. As the wheel spins, the height traces out a smooth, repeating curve — a sine wave . Circular motion at a steady speed makes height rise and fall in a repeating wave — that wave is the sine. Drag the wheel around, or slide the angle. At every angle the rider sits at height , where the axle is c = 24 m up and the radius is r = 12 m. Watch the seat and the dot on the wave move together — the wave is just a record of the height at each angle. At the top the height peaks, at the bottom it bottoms out, and after one full turn it repeats — that is what periodic means. The wave's shape is set by the wheel. The radius r decides how far the height swings above and below the middle — the amplitude . The axle height c decides the line the height waves around — the midline . Change each and watch the wave stretch and lift.

This is the written version of the interactive lesson above. See the full Algebra 2 course.