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)

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

(1.0)

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

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

(1.1)

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

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

(1.2)

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

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

(1.3)

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

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

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

(1.4)

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

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

(1.5)

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

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

(1.6)

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

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MaintenanceBot (discuss • contribs) 03:41, 11 November 2013 (UTC)