Question

In Steinhatchee in July, high tide is at noon. The water level is 5 feet at high tide and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Steinhatchee's water level in July as a function of time (t). f(t) = 6 cos pi over 2 t + 2 f(t) = 2 cos pi over 2 t + 3 f(t) = 2 cos pi over 6 t + 3 f(t) = 6 cos pi over 6 t + 2

Answer 1

f(t)= 2 cos pi/6t + 3

Answer 2

The equation for Steinhatchee's water level in July as a function of time (t) is:

`f(t)=2 \cos ((\pi)/(6)t)+3`

Explanation:

It is given that:

The function f(t) is modeled by a cosine curve.

• The water level is 5 feet at high tide and 1 foot at low tide.

That means the maximum value attained by the function is 5 and the minimum value attained by the function is -1.

Also,

• The next high tide is exactly 12 hours later.

This means that the period of the cosine function is: 12

Hence, the property as discussed above is satisfied by the function:

`f(t)=2 \cos ((\pi)/(6)t)+3`

( Since, when t=0 we obtain the high tide.

(As the function gives the value 5.

Also at t=3 , we obtain a low tide.

Since the function gives the value -1.

Also the period of this function is: 12 )