Sinusoidal Functions Help

In summary, a sinusoidal function is a mathematical function that describes a repeating wave-like pattern and is typically represented by the formula f(x) = A sin (Bx + C) + D. The difference between a sine and cosine function is that they have a 90-degree phase shift. To graph a sinusoidal function, you can plot points using the formula and the values of A, B, C, and D. Sinusoidal functions can model real-life phenomena such as sound waves, light waves, tides, and pendulum motion, and they can be used in problem-solving to analyze data and solve real-world problems related to waves, vibrations, and oscillations.
  • #1
Sonny18n
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1. Homework Statement

A graph of y=f(x) is shown. Find the following function values and justify your answers.

f(30)=
f(-14)=

Homework Equations

The Attempt at a Solution


I know the graph is periodic, I know it's max and min, and I know it's amplitude because of that. But I don't know what the 30 or -14 is supposed to mean to me or how I'm suppose to "justify" my answer[/B]
 
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  • #2
Sonny18n said:
View attachment 80886 1. Homework Statement
A graph of y=f(x) is shown. Find the following function values and justify your answers.

f(30)=
f(-14)=

Homework Equations

The Attempt at a Solution


I know the graph is periodic, I know it's max and min, and I know it's amplitude because of that. But I don't know what the 30 or -14 is supposed to mean to me or how I'm suppose to "justify" my answer[/B]

It looks to me like what you are supposed to conclude from the graph is that f(x+4)=f(x). That's periodic. So f(-14)=f(-10)=f(-6)=f(-2). The last value you can read off from the graph. Patterns like that.
 
  • #3
f(30) and f(-14) are the values of the function calculated in x=30 and x=-14.
You said that the graph is periodic, so it means that the graph repeat itself with perod 5.
now you should obtain the two values.
 
  • #4
Yes, Dick is right, the period is 4
 
  • #5
Pierce610 said:
Yes, Dick is right, the period is 4
(It is possible for you to Edit post #3. )
 
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Likes Pierce610
  • #6
Now no more; I'll do it in future if I should realize in time to have to correct my post
 
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1. What is a sinusoidal function?

A sinusoidal function is a mathematical function that describes a repeating wave-like pattern. It is typically represented by the formula f(x) = A sin (Bx + C) + D, where A, B, C, and D are constants that determine the amplitude, period, phase shift, and vertical shift of the function, respectively.

2. What is the difference between a sine function and a cosine function?

A sine function is a type of sinusoidal function that starts at the origin and moves upward, while a cosine function starts at its maximum value and moves downward. In other words, they are the same function but with a 90-degree phase shift.

3. How do you graph a sinusoidal function?

To graph a sinusoidal function, plot several points using the formula f(x) = A sin (Bx + C) + D. The value of B determines the period, or length of one cycle, of the function. The value of A determines the amplitude, or maximum height, of the function. The value of C determines the horizontal shift, and the value of D determines the vertical shift.

4. What real-life phenomena can be modeled using sinusoidal functions?

Some examples of real-life phenomena that can be modeled using sinusoidal functions include sound waves, light waves, tides, and the motion of a pendulum. Sinusoidal functions are also used in fields such as engineering, physics, and economics to analyze and predict data.

5. How can sinusoidal functions be used in problem-solving?

Sinusoidal functions can be used in problem-solving to model and analyze various situations. They can help determine maximum and minimum values, find the period and amplitude of a function, and predict future values based on known data. Additionally, sinusoidal functions can be used to solve real-world problems involving waves, vibrations, and oscillations.

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