Link Between Circular & Planar Domains

[ragavcit]

Hi,
Why did people link a circular and a planar domain?To be more specific,the term angular frequency is related to a circular domain and we use it to describe a sine wave which is in a planar domain??

 

[HallsofIvy]

Any precise definition of the sine and cosine functions should make no reference to angles. Unfortunately engineers tend to think of them in (old) trigonmetric terms and use the word "angle" where it really doesn't apply. You could ask the same question about the "phase angle" in electric circuits.

 

[Tac-Tics]

It's not clear what you are asking exactly.

In mathematics, we don't use the term angular frequency. It's more of a physics term. It's more appropriate in math to use the period of a function, which is a number T such that f(x) = f(x+T) for all numbers x.

Also, there's nothing planar or circular about a sine wave. Sine is just a function. It maps numbers to other numbers. It has an interesting physical significance in geometry, of course: when the point (1, 0) travels a distance x along the circumference of a circle with radius 1, and the point ends up at the coordinate (cos x, sin x).

It sounds like you might be getting hung up on the graph of a sine wave, which is the familiar wobbly line that alternates between 1 and -1 forever along the x axis. But that is simply one possible representation of sine, and not sine itself.