Instantaneous current in stator of 3 phase IM

[rishi kesh]

I am studying induction motors and i have equation for instantaneous value of current flowing in each phases.(please check to image below).I can see that its it the form Im.cosωt
But isn't it supposed to be Im.sinωt ?because that's how we find all instantaneous parameters like voltage and power.we have homework regarding the same. Please explain it carefully considering I am first year engineering student.

 

[anorlunda]

The only difference between sin and cos is the reference phase (what we call angle zero). So if you are talking about the "form", sin and cos are the same thing.

 

[rishi kesh]

The only difference between sin and cos is the reference phase (what we call angle zero). So if you are talking about the "form", sin and cos are the same thing.

Please explain this to me in more detail if possible.sorry for inconvinience.

 

[anorlunda]

For more detail, try this article. https://en.wikipedia.org/wiki/Sine

 

[cnh1995]

I can see that its it the form Im.cosωt
But isn't it supposed to be Im.sinωt ?because that's how we find all instantaneous parameters like voltage and power.

As anorlunda said, they are just shifted by 90 degrees. It doesn't make any difference if you use cos instead of sine. All the other equations will change accordingly.
For example, if the current through an inductor is I_msin(ωt), the voltage across the inductor will be Ldi/dt=ωLI_mcos(ωt). Here the current is lagging the voltage by 90° (which is expected.)
If the current were I_mcos(ωt), the voltage across the inductor would be -ωLI_msin(ωt). The current still lags the voltage by 90° .

Work out some examples on your own and you'd realize the importance of sine wave in ac electricity. The derivatives and integrals of a sine wave are also sine waves with a phase-shift (cos is sine with 90 degrees phase shift). This important property simplifies the math required to analyse ac circuits. (Although it "simplifies" the math, it's called "complex" analysis).