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My intuition is that the $2\pi$ term in the sinusoidal signal equation:

$$x(t) = \sin(2\pi\,f\,t)$$

Is indicative of the fact that this signal can be described as movement around a circle, is that correct?

And the sin component is describing the path it takes about that circle?

*Due to a lack of reputation I'm unable to properly tag this inquiry, would someone please help me remedy that.

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up vote 0 down vote accepted

The $2\pi$ in the equation is to make the $f$ represent cycles per second (assuming $t$ is in seconds). For example, if $f=10$, then the sine wave $\sin(2\pi\,10\,t)$ will crest 10 times from $t=0$ to $t=1$.

Circles can always be used to represent sine waves. The height of a person on a Ferris wheel is is a sine wave, even though their motion is a circle. See the top answer to this question.

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ah that's very nice, thank you for that. But you know, sometimes I also see this shark-tooth looking pattern, would that one also be able to be represented by 2pi? Isn't that what, kind of, hooks it around the circle that it's rotating around? Does that make any sense? – user146324 May 1 '14 at 15:38
how did you make those nice symbols? – user146324 May 1 '14 at 15:44
@matthias.anglicus If you put your symbols inside of dollar signs you can use latex like : \$\sin(2\pi f t)\$, and I think the easiest way to learn latex is to right click on other people's post and choose "show math as $\rightarrow$ tex commands". – DanielV May 1 '14 at 20:54
@matthias.anglicus I think the shape you are referring to is called a saw tooth function, check it out on wikipedia. – DanielV May 1 '14 at 20:55

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