y = A sin B(x − C) + D
or in this case T = A sin B(t − C) + D.
The period is 12 months, so 2π/B = 12 and hence B = π/6.
The amplitude = (max − min)/2 = (21 − 8)/2 = 6.5, so A = 6.5.
The principal axis is midway between the maximum and minimum values, so D = (max + min)/2.
So, the model is T = 6.5 sin (π/6)(t − C) + 14.5
