Applications of sinusoidal functions.

In summary, the maximum depth of the water is 4.9 meters and it occurs at 7:06am and 7:30am. This is found by substituting the maximum depth of 4.9 into the equation for h and solving for t. The first equation used, 4.9 = 1.8sin 2pi [(t-4)/12.4] + 3.1, was incorrect because of missing parentheses and the substitution of the maximum depth as the y value without explanation.
  • #1
anonymous12
29
0

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
 
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  • #2
anonymous12 said:

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
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
Mark44 said:
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
anonymous12 said:
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
anonymous12 said:
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.
anonymous12 said:
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
 

1. What are sinusoidal functions?

Sinusoidal functions are mathematical functions that describe a repeating pattern or oscillation, similar to a sine or cosine wave. They are commonly used to model real-world phenomena, such as sound waves, electromagnetic waves, and periodic motion.

2. What are the applications of sinusoidal functions?

Sinusoidal functions have numerous applications in fields such as physics, engineering, and mathematics. They are used to model and analyze periodic processes, such as the motion of a pendulum, the alternating current in an electrical circuit, and the vibrations of a guitar string.

3. How are sinusoidal functions graphed?

Sinusoidal functions are graphed using a coordinate plane, where the horizontal axis represents the input or independent variable, and the vertical axis represents the output or dependent variable. The graph of a sinusoidal function is a smooth, continuous curve that repeats itself over regular intervals.

4. What is the amplitude of a sinusoidal function?

The amplitude of a sinusoidal function is the distance between the midline and the maximum or minimum values of the function. It represents the height or depth of the oscillation and is equal to half of the difference between the maximum and minimum values.

5. How are sinusoidal functions used in real life?

Sinusoidal functions are used in a variety of real-life applications, such as predicting tides, analyzing sound and light waves, and designing musical instruments. They are also used in industries such as telecommunications, signal processing, and robotics.

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