Question

I would like help with the question. It's part of my assigment, but I have trouble with this type of math. If someone understands, can you explain it to me as well? For future reference?

In Panama City in January, high tide was at midnight. The water level at high tide was 9 feet and 1 foot 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 January for Panama City as a function of time (t).

Answer 1

So this in the formation I have gathered from what you have above:
high tide (or max value of the cosine curve) is 9ft
low tide (or min value of the cosine curve ) is 1ft

We are given at 24hours we have 9ft tide coming in
And then 12 hours later we have again a 9ft tide coming in

do you think you can plot the points given so far?

Answer 2

Thank you for replying.

I'm really not certain where to start with this one. The highest point will be at 9,0, and the lowest at 1,0? And 24 is how long the curve will be from start to finish?

Answer 3

do you understand that time is the x-axis?
and the the height of the tide is the y-axis?

if so then why aren't your points consider the time value and the related height of tide value?

Answer 4

that is one point I gave you is (24,9)
another point I gave you is (24+12,9) since 12 hours later we have the hightide thing occurring again

Answer 5

12 midnight is 24 hours into the day don't you agree?

Answer 6

for example:
1 am is 1 hours
2 am is 2 hours
3 am is 3 hours
4 am is 4 hours
5 am is 5 hours
6 am is 6 hours
7 am is 7 hours
8 am is 8 hours
9 am is 9 hours
10 am is 10 hours
11 am is 11 hours
12 am is 12 hours
01 pm is 13 hours
02 pm is 14 hours
03 pm is 15 hours
04 pm is 16 hours
05 pm is 17 hours
06 pm is 18 hours
07 pm is 19 hours
08 pm is 20 hours
09 pm is 21 hours
10 pm is 22 hours
11 pm is 23 hours
12 pm is 24 hours (remember 1 whole day is equal to 24 hours?)

Answer 7

I think a visual would help you ....

But you can also do this without a visual

Answer 8

If you want me to help you a nice place for me to do that is with the visual I'm asking you to create.

Answer 9

Do you see the draw tool below?

Answer 10

I will draw the y=cos(x) curve
because I think it will help to build our equation for your curve...

this is what one period (which is equal to 2pi) looks like for y=cos(x)
notice the period starts with a max and ends with a max
so your problem actually gives you the period number


y=a*cos(b(x-c))+d
|a| is the amp
2pi/|b| is the period
c is the phase shift number
d is the vertical shift