You have the following function for the high and low tide of a beach in California:
F(t) = 8·coscos(10t) + 8
a) Take into account that the maximum value that cosine can have is 1, then, the maximum value that the first term of the function can acquire is 8·1 = 8.
Then, the maximum value of the function is:
F_max = 8·1 + 8 = 8 + 8 = 16
The highest the water gets is 16 feet.
b) Consider that the period of cos10t is:
T = 2π/10 = π/5
now, consider that the cosine of cos10t, will have one half of the period of cos10t. Then, the period of coscos10t is π/10.