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?
The water level varies from 12 inches at low tide to 64 inches at high tide
so the center line is at y=(12+64)/2 = 38
The amplitude is (64-12)/2 = 26
1/4 period is 5.5 hours, so the period is 22 hours
The function starts at a minimum at 8 a.m. (t=0), so
y = 38 - 26cos(π/11 t)
Yes, you are correct. 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:
h(t) = 38 - 26cos(π/11 t)
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:
h(t) = 26cos(π/5(t-8))
where h(t) represents the water level in inches above or below the water level at time t in hours since 8 am.