# Sine Wave Functions

Discussion in 'Homework Help' started by m4yh3m, May 13, 2004.

1. ### m4yh3m Thread Starter Senior Member

Apr 28, 2004
186
42
if a sine wave is

f(x)=sin x

x = phase?

Jan 19, 2004
220
0
yes.. x is the phase
usually phase is the measure of time lead or lag of a wave/particle with respect to another measured to an reference(origin).. for mathematical purposes it is measure in terms of and angle.

3. ### Dave Retired Moderator

Nov 17, 2003
6,960
145
x is not the phase, x is the variable of the function as you have defined f(x).

If you look at the following function:

f(x) = Sin (Θ±φ)

Where x = (Θ±φ)

Θ is the angle which is subdefined in the context of your function (for example, for a phasor Θ = ωt)

And φ is the phase.

4. ### m4yh3m Thread Starter Senior Member

Apr 28, 2004
186
42
so what's the difference between

f(x)= Vpk sin Θ
f(x)= Vpk sin ωt
f(x)= Vpk sin (ωt +Θ)

?

5. ### Dave Retired Moderator

Nov 17, 2003
6,960
145
Just the notation.

In all examples you have defined x as the variable, however you need to say the following for the expression to make sense:

1) x = Θ

2) x = ωt

3) x = ωt ± Θ (although in this example you have defined the phase with Θ, which is not considered standard practice, generally use φ or ø)

However it is not really correct to define f(x) in this way as you are declaring x as a variable of the function where the function operates in other terms, i.e. Θ, t, ω and φ (this is more my fault for using this notation in my previous reply). More precisely, you should say:

v(t) = Vpk Sin (ωt ± φ)

Which says the sinusoidal voltage operates as a function of time with angular velocity ω and phase angle φ.

6. ### m4yh3m Thread Starter Senior Member

Apr 28, 2004
186
42
thank you very much for the clarification.