Is There an Error in Converting I2 from Phasor to Time Domain?

[Evales]

So we're converting these currents from phasor to time domain with ω=4.

I understand I₁, but not how the lecturer got I₂, is this an error with the notes?

We have these phasors:

Which are converted to this time domain (respectively):

Any help is much appreciated.

 

[gneill]

Hmm. I₂ doesn't look correct to me for a couple of reasons. First, if the angle had been adjusted by adding 360°, giving -160.6 + 360 = 199.4°, then the result should show it as a positive phase angle, not negative. Second, the convention is to specify phase angles in the range +/- 180°, and 199.4° falls outside this range.

 

[NascentOxygen]

Check I₂. Possibly it was given as 3.254 ∠160.6°
and lecturer is converting all angles to lagging.