# User talk:Egm4313.s12.team1.silvestri

First edit. Here's to seeing what will happen.

playing with equations

First, we identify the property of periodic functions, as shown on p9-2 of the notes, equation (1)

 ${\displaystyle \displaystyle {f(x+np)=f(x)}}$ (1.0)

So for ${\displaystyle \cos n\omega x}$, the following determines the smallest period.

 ${\displaystyle \displaystyle {\cos(n\omega x)}}$ (1.1)

We then add ${\displaystyle 2\pi }$ to see a final expression that will be equal to ${\displaystyle \displaystyle {f(x+np)=f(x)}
}$

 ${\displaystyle \displaystyle {\cos(n\omega x+2\pi )}}$ (1.2)

We then pull out a term that leaves an x plus a number (our period) inside the trigonometric function, cosine.

 ${\displaystyle \displaystyle {\cos[n\omega (x+{\frac {2\pi )}{n\omega }}]}}$ (1.3)

This means the smallest period is ${\displaystyle frac{2\pi }{n\omega }}$.

For ${\displaystyle \sin n\omega x}$, the following determines the smallest period.

 ${\displaystyle \displaystyle {\sin(n\omega x)}}$ (1.4)

We then add ${\displaystyle 2\pi }$ to see a final expression that will be equal to ${\displaystyle \displaystyle {f(x+np)=f(x)}
}$

 ${\displaystyle \displaystyle {\sin(n\omega x+2\pi )}}$ (1.5)

We then pull out a term that leaves an x plus a number (our period) inside the trigonometric function, cosine.

 ${\displaystyle \displaystyle {\sin[n\omega (x+{\frac {2\pi )}{n\omega }}]}}$ (1.6)

This means the smallest period is ${\displaystyle frac{2\pi }{n\omega }}$, just as for its cosine equivalent.

Egm4313.s12.team1.silvestri 20:09, 25 January 2012 (UTC)

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Crochet.david (talk) 12:59, 26 February 2012 (UTC) Alpha = .5