When the time t is measured in hours the period T is when cos(85t) again has the same value for t+T, where T is the period.
Let t=0 (7am) then cos(85t)=1. The next time cos(85t) is equal to 1 is when 85T=2π=6.2632. So T=2π/85=0.07392 hours approx. Converted into seconds this period is 4.4352 seconds approx.
