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Last modified: January 26, 2018
Amplitude, Period and Phase
---------------------------
y = Asin(Bx - C) + D and y = cos(Bx - C) + D
A = Amplitude = (max - min)/2
B = Stretch/shrink on the x-axis. (It compresses or expands the graph.)
B has the following relationship with the period:
B = 2π/T so T = 2π/B
C/B = The phase shift (left (if C/B is neg.) or right (if C/B is pos.))
D = The vertical shift of the graph
Interval (complete cycle) = (C, C + 2π/B)
Ex. y = 1 + 3sin 2(t - π/2)
y = 3sin(2t - π) + 1
A = 3
B = 2
C = π
D = 1
Period = 2π/B = 2π/2 = π
Phase shift = C/B = π/2 (shifted right)
vertical shift = 1
Interval (complete cycle) = (π, 2π)