Sine Wave Functions

if a sine wave is

f(x)=sin x

x = phase?

 

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.

 

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.

 

so what's the difference between

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

?

 

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.

 

thank you very much for the clarification.