During the first two rotations, at what time and height does the instantaneous rate of change does the sinusoidal equation ''h = 25 - 22 cos(2π/82 t)'' have the greatest positive value?
cos(kx) has a period of 2π/k
so, cos(2π/82 t) has a period of 82
it will be at a minimum mid-period, when t=41, 123, ...
Thus h will be at a max when t = 41,123, ... 41 + 82n for any integer n