Sinusoidal functions
y = a sin b(x − c) + d: amplitude |a|, period 360°/b (or 2π/b in radians), phase shift c and midline y = d.
A worked example
A Ferris wheel 40 m across, centre 22 m up, one turn every 2 min, starting at the bottom: amplitude 20, midline 22, b = 2π/2 = π, shifted a quarter turn right: h = 20 sin π(t − 0.5) + 22. At t = 0, h = 20(−1) + 22 = 2 m.
The mistake people actually make
The amplitude is half the distance from minimum to maximum, not the whole distance. Set the calculator to the mode the model uses.