In Pensacola in June, high tide was at noon. The water level at high tide was 12 feet and 2 feet at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in June for Pensacola as a function of time (t).

Question

anonymous · Answer

@jim_thompson5910 Sorry to keep calling you!  You're the only person I've found who will respond AND teach.  If you don't feel like answering, it's all right.  You've done more than your share :)

compassionate · Answer

Hey, I live in Pensacola. Kudos!

anonymous · Answer

Haha, I live near clearwater.

compassionate · Answer

In Pensacola?

jim_thompson5910 · Answer

how far did you get 1lorax2 ?

anonymous · Answer

Isn't Pensacola in FL?

compassionate · Answer

Oh, Clearwater, FL, you're about five hours from me.

anonymous · Answer

Like Clearwater Beach, near tampa

anonymous · Answer

So... Do you know how to do the problem?

anonymous · Answer

I don't mean to be rude, but I've been doing math since 4 today, and my brain is pretty much oatmeal.

anonymous · Answer

@Compassionate

scorcher219396 · Answer

So in any given trig function where y=Acos(Bx-C)+D
A is the amplitude, the period is (normal period/B), D is vertical shift, and C/B is phase or horizontal shift

With the information you're given, you know the amplitude is 5 (since max-min is 12-2, then divided by 2) and it has also been shifted up 7
The period is 12, so 12=(2pi)/B, and B=pi/6
Since it's high tide at noon and you're using cosine, you don't have to worry about a phase shift here

So with that, you should get y=5cos((pi/6)x)+7