# Applications of sinusoidal functions.

## Homework Statement

At a seaport, the depth of the water h metres at time t hours during a certain day is given by this formula:

Q: What is the maximum depth of the water? When does it occur?

## Homework Equations

h = 1.8 sin 2pi [(t - 4)/12.4] + 3.1

## The Attempt at a Solution

4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1
1.8sin2pi = 0
4.9 - 3.1 = (t-4)/12.4
1.8 = (t-4)/12.4
1.8 x 12.4 = t - 4
22.32 + 4 = t
26.32 = t

That answer is wrong even when i convert from 24 hour clock to the 12 hour clock.
The correct answer is 7:06a.m and 7:30a.m

Last edited:

Mark44
Mentor

## Homework Statement

At a seaport, the depth of the water h metres at time t hours during a certain day is given by this formula:

## Homework Equations

h = 1.8 sin 2pi [(t - 4)/12.4] + 3.1

## The Attempt at a Solution

4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1
1.8sin2pi = 0
4.9 - 3.1 = (t-4)/12.4
1.8 = (t-4)/12.4
1.8 x 12.4 = t - 4
22.32 + 4 = t
26.32 = t

That answer is wrong even when i convert from 24 hour clock to the 12 hour clock.
The correct answer is 7:06a.m and 7:30a.m
If the correct answers are 7:06am and 7:30am, what is the question? There is nothing in your problem statement that asks a question.

Oops. Here's the question:

Q: What is the maximum depth of the water? When does it occur?

Mark44
Mentor
Why does the "correct" answer not give the maximum depth?

And why is your first equation 4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1? Where did that 4.9 come from?

Why does the "correct" answer not give the maximum depth?

And why is your first equation 4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1? Where did that 4.9 come from?

Well the original equation is : h = 1.8 sin 2pi [(t - 4)/12.4] + 3.1
Since it's a sinusoidal function, the maximum height of that this sinusoidal function can achieve is 4.9. You get that by adding 3.1 + 1.8 = 4.9

And my first equation is 4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1 because I substituted the 4.9 as the y value since we want to find out what time the depth of the water is at its max (4.9)

Mark44
Mentor
Well the original equation is : h = 1.8 sin 2pi [(t - 4)/12.4] + 3.1
I think if you'll check the book, you'll find that you are missing some parentheses. This should be 4.9 = 1.8sin (2pi (t-4)/12.4]) + 3.1
Since it's a sinusoidal function, the maximum height of that this sinusoidal function can achieve is 4.9. You get that by adding 3.1 + 1.8 = 4.9
Then you should say something to establish this. The reason is that the maximum value of the sine function is 1, so the maximum value of 1.8*sin(whatever) + 3.1 is 4.9.
And my first equation is 4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1 because I substituted the 4.9 as the y value since we want to find out what time the depth of the water is at its max (4.9)
4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1
4.9 - 3.1 = (t-4)/12.4
1.8 = (t-4)/12.4
1.8 x 12.4 = t - 4
22.32 + 4 = t
26.32 = t