The water level varies from 12 inches at low tide to 64 inches at high tide. Low tide occurs at 8
am and high tide occurs at 1:30 pm. What is a cosine function that models the variation in inches
above and below the water level as a function of time in hours since 8 am? (5 points)
The cosine function that models the variation in inches above and below the water level as a function of time in hours since 8 am is:
f(t) = 26cos(2π/6 * (t - 8))
Where:
- f(t) represents the inches above and below the water level at time t
- t represents the time in hours since 8 am
- 26 is the amplitude of the cosine function, which is half the difference between the high tide and low tide (64 - 12)/2 = 26
- 2π/6 is the frequency of the cosine function, as there are 6 hours between low tide and high tide
- (t - 8) represents the time shift, as low tide occurs at 8 am
This cosine function will oscillate between -26 and 26 inches every 6 hours, with the maximum at high tide (1:30 pm) and the minimum at low tide (8 am).