# Thread: Amplitude, Period, and Displacement?

1. ## Amplitude, Period, and Displacement?

Hi all...after finishing my homework tonight I decided to keep going in the chapter to get ahead. Yeah, I was also enjoying myself too!

The next part of the chapter deals with Amplitude, Period, and Displacement.

Here is a sample question from the book.

Determine the amplitude, period, and displacement of the given function. Then sketch the graph of the function.

$\displaystyle y = 2\ cos \displaystyle \left(x\, + \frac{\pi}{12}\right)$

Could someone break this type of problem down to it's parts so I can work my way through this section of the chapter?

Once again, I'm taking my math online which means I've basicly become my own teacher.

2. Hey,
you could plot the function against the graph of $y = cosx$, Translate the graph in stages, i.e change the amplitute $y = 2cosx$ and observe the result. Then you can look at the graph of $y = cos(x+\frac{\pi}{12})$ (Phase shift of $\frac{\pi}{12}$.), how to draw $y = 2cos(x+\frac{\pi}{12})$ should become obvious.

3. Originally Posted by Oiler
Hey,
you could plot the function against the graph of $y = cosx$, Translate the graph in stages, i.e change the amplitute $y = 2cosx$ and observe the result. Then you can look at the graph of $y = cos(x+\frac{\pi}{12})$, how to draw $y = 2cos(x+\frac{\pi}{12})$ should become obvious.
Thanks for responding Oiler. I think first I need to understand the proper way to find the amplitude, period, and displacement of the given function. After that I know I could use the calculator to see the graph.

Does that make sense?

4. Given, $f(x) = A sin(Bx-C) + D$
The Amplitude is $A$
The vertical shift is $D$
The period will be given by $\frac{2\pi}{B}$
And you can work out the frequency by $f = \frac{1}{period} = \frac{1}{\frac{2\pi}{B}}=\frac{B}{2\pi}$
The phase shift is $\frac{C}{B}$
Hopefully that helps..

5. Originally Posted by Oiler
Given, $f(x) = A sin(Bx-C) + D$
The Amplitude is $A$
The vertical shift is $D$
The period will be given by $\frac{2\pi}{B}$
And you can work out the frequency by $f = \frac{1}{period} = \frac{1}{\frac{2\pi}{B}}=\frac{B}{2\pi}$
The phase shift is $\frac{C}{B}$
Hopefully that helps..
Yes that helps a lot. I have added that to my notes.

So after looking this over this is what I came up with.

Determine the amplitude, period, and displacement of the given function. Then sketch the graph of the function.

$\displaystyle y = 2\ cos \displaystyle \left(x\, + \frac{\pi}{12}\right)$

The Amplitude is = $2$

The period = $\frac{2\pi}{1}$ = $2\pi$

The displacement = $-\frac{\pi}{\frac{12}{1}}$ = $-\frac{\pi}{12}$

6. I've worked through about ten like the previous post and they were progressively getting harder and then a came upon this one...

Find the function and graph it for a function of the form $\displaystyle y = 7\ sin \displaystyle \left(7x\ + c)\right$ that passes through $\left(-\frac{\pi}{5}, 0)\right$ and for which $c$ has the smallest possible positive value.

This one has me a bit intimidated.

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