# Amplitude, Period, and Displacement?

• Mar 19th 2011, 07:39 PM
Smokinoakum
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.

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

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.
• Mar 19th 2011, 07:54 PM
Oiler
Hey,
you could plot the function against the graph of $\displaystyle y = cosx$, Translate the graph in stages, i.e change the amplitute $\displaystyle y = 2cosx$ and observe the result. Then you can look at the graph of $\displaystyle y = cos(x+\frac{\pi}{12})$ (Phase shift of $\displaystyle \frac{\pi}{12}$.), how to draw $\displaystyle y = 2cos(x+\frac{\pi}{12})$ should become obvious.
• Mar 19th 2011, 07:58 PM
Smokinoakum
Quote:

Originally Posted by Oiler
Hey,
you could plot the function against the graph of $\displaystyle y = cosx$, Translate the graph in stages, i.e change the amplitute $\displaystyle y = 2cosx$ and observe the result. Then you can look at the graph of $\displaystyle y = cos(x+\frac{\pi}{12})$, how to draw $\displaystyle y = 2cos(x+\frac{\pi}{12})$ 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?
• Mar 19th 2011, 08:08 PM
Oiler
Given, $\displaystyle f(x) = A sin(Bx-C) + D$
The Amplitude is $\displaystyle A$
The vertical shift is $\displaystyle D$
The period will be given by $\displaystyle \frac{2\pi}{B}$
And you can work out the frequency by $\displaystyle f = \frac{1}{period} = \frac{1}{\frac{2\pi}{B}}=\frac{B}{2\pi}$
The phase shift is $\displaystyle \frac{C}{B}$
Hopefully that helps..
• Mar 19th 2011, 08:11 PM
Smokinoakum
Quote:

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

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

The Amplitude is = $\displaystyle 2$

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

The displacement = $\displaystyle -\frac{\pi}{\frac{12}{1}}$ = $\displaystyle -\frac{\pi}{12}$
• Mar 19th 2011, 10:30 PM
Smokinoakum
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 $\displaystyle \displaystyle y = 7\ sin \displaystyle \left(7x\ + c)\right$ that passes through $\displaystyle \left(-\frac{\pi}{5}, 0)\right$ and for which $\displaystyle c$ has the smallest possible positive value.

This one has me a bit intimidated.