Question

2. At the Bay of Fundy, the difference between high and low tide is 8m and the time between high tides is 12 hours. At midnight, the water is at high tide. Write a sine function that models the water level over time t.

Answer 1

Answer:
`y=4sin((\pi )/(6) x+(\pi )/(2) )`

Explanation:

We start from the general form of the sine function which is:

`y=a sin(bx+c)`

where

Amplitude= IaI=
`(8)/(2)`=4( which is the maximum value we have above the 0 axis)

Period=
`(2\pi )/(b)`

Period=12 (space between high tides)

Isolating b:

`b=(1)/(6) \pi`

Horizontal shift = c (Normally the function starts at 0 but in the excercise we have at midnight hight tide this meaning the function is at its maximum value so we need to move it a quarter of the period so it will have maximum value at t=0)

`c=(\pi )/(2)`

then

`y=4sin((\pi )/(6) x+(\pi )/(2) )`