Can someone explain why i1 doesn't lead i3 by 345 degrees?

 

Try drawing the three currents as vectors on a polar plot.

 

First, get all three into the same form, namely

i_n(t) = I_N cos(ωt + θ_n)

Then determining how much one leads another becomes trivial.

 

In i_n(t) = I_N sin(ωt + θ_n) what is the range of θ_n?

-180 degrees to 180 degrees or 0 to 360 degrees?
I got two different results with the question i1(t) leads i3(t).
If θ_n is from -180 to 180 degrees then i1(t) leads i3(t) by 165 degrees.
If θ_n is from 0 to 360 degrees then i1(t) leads i3(t) by -195 degrees.

 

In i_n(t) = I_N sin(ωt + θ_n) what is the range of θ_n?

-180 degrees to 180 degrees or 0 to 360 degrees?
I got two different results with the question i1(t) leads i3(t).
If θ_n is from -180 to 180 degrees then i1(t) leads i3(t) by -165 degrees.
If θ_n is from 0 to 360 degrees then i1(t) leads i3(t) by -195 degrees.

It shouldn't matter what range you choose. Either way, you may need to normalize the answer, but the answers should be the same modulo 360°.

 

I realise I made a mistake. The first case is 165 degrees and the second is -195 degrees.
And as you said both are correct. There is an infinite number of the correct answers here?

 

I realise I made a mistake. The first case is 165 degrees and the second is -195 degrees.
And as you said both are correct. There is an infinite number of the correct answers here?

Yes, though common practice is to reduce it to less than one complete revolution in either direction and to normally restrict even that to a total range of just one revolution overall.