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

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SUMMARY

The discussion centers on the conversion of phasors to the time domain, specifically focusing on the current I2 with a frequency of ω=4. Participants express confusion regarding the lecturer's conversion of I2, questioning its accuracy due to the phase angle being outside the conventional range of +/- 180°. The correct representation of I2 should be 3.254 ∠160.6°, and the conversion should maintain the positive phase angle convention. This indicates a potential error in the lecturer's notes regarding the treatment of phase angles.

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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:
xKnOJ.png


Which are converted to this time domain (respectively):
oF3SU.png


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

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