Question

The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:30 p.m. 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 9:15 a.m.?

Answer 1

from the data:
difference between high tide and low tide
= 15:30 - 9:15 = 3:15
so the period = 6:30 or 6.5 hours
the bot equation would make it as 6 hours

period = 2π / k
6.5 = 2π/k
k = 2π/6.5 = 4π/13

so the equation would be:
y = 20 cos (4π/13 t) + 32

graph this using:
desmos.co m/calculator , to see that it is correct

(of course after cutting and pasting <b>desmos.co m/calculator</b>
you know you have to delete the space to fool this webpage)