Applications of sinusoidal functions.

  • #1

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:

Answers and Replies

  • #2
34,697
6,399

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.
 
  • #3
Oops. Here's the question:


Q: What is the maximum depth of the water? When does it occur?
 
  • #4
34,697
6,399
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?
 
  • #5
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)
 
  • #6
34,697
6,399
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
 

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