What does y = A sin(B(x − C)) + D model?
Any simple periodic signal. A is the amplitude, B sets the period, C is the horizontal (phase) shift and D is the midline the wave oscillates about.
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Modelling Periodic Phenomena
Explore y = A sin(B(x − C)) + D and read off amplitude, period, phase shift and midline for a periodic model, in degrees or radians.
y = A sin(B(x − C)) + D — amplitude |A|, period 360°/B, midline D
Angle unit
Frequently asked questions
How do I read off the features?
Amplitude = |A|; period = 360°/B (or 2π/B in radians); midline y = D, so maximum = D + |A| and minimum = D − |A|; the curve shifts right by C.
Can you show a worked example?
y = 2 sin(2(x − 30°)) + 1 has amplitude 2, period 360°/2 = 180°, midline y = 1, maximum 3 and minimum −1. In radians the period is π ≈ 3.1416 rad.
How do I fit one to data?
Read the midline as the average of max and min, the amplitude as half their difference, the period from peak-to-peak spacing, and the shift from where a peak occurs.
Where is it used?
Tides, daylight hours, monthly temperature, AC voltage and many biological rhythms are all modelled with this single sinusoid.