The Math Meridian
Back to Periodic and Sinusoidal Functions

Sinusoidal models: Ferris wheels, tides and daylight

Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.

Useful for: MCR3U MCF3M IB Math AI SL & HL AP® Precalculus

Learn it Build the model from the story: the axis is the average level, the amplitude is half the change, the period is one full cycle. Then substitute a time to predict, or solve to find when a height is reached.

Example: A Ferris wheel of radius 15 m has its centre 17 m up and turns once every 60 s. A rider starts at the bottom.

  1. h(t) = −15 cos(6t) + 17 (degrees, since 360°/60 = 6).
  2. At t = 20 s: h = −15 cos 120° + 17 = 24.5 m.

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