Question

In Crescent Moon Bay in July, high tide is at 3:00 pm. The water level is 6 feet at high tide and 2 feet 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 Crescent Moon Bay's water level in July as a function of time (t).

Answer 1

Correct me if I’m wrong, but the answer should be f(t) = 2 cos pi over 6 t + 4.

Explanation:

Answer 2

`F(X) =  2 cos ((pi)/(6) .x ) + 4`

Explanation:

The high tide which is 2 feet above than 4 ft

and while low tide which is 2 ft below than 4 ft

-If the function is f(x), then I want x = 0

to x = 12 to equal 1 period ( 12 hrs )

So function is

f(x) = 2 cos (k x + 4

f(12) = 2 cos(k . 12) + 4

`k. x  = 2 \pi`

`k . 12 = 2 \pi`

`k = (\pi)/(6)`

Now
`F(X) =  2 cos ((pi)/(6) .x ) + 4`

plot for 1 period of function

from x =0 to x =12