Usually, phasors are represented by Acos(ωt + φ) where φ is the phase angle. Using this convention, we need to convert sin(ωt) into cos(ωt - 90) to get its phase angle like this thumbnail on a YouTube video.
But in EE, the AC sources are usually sinusoids and back when I first studied about phasors in physics, they were introduced as Asin(ωt + φ) with φ being the phase angle.
What is the correct way to represent sine waves (say 120sin(120πt)) in polar form?
All that matters is the phase difference. There is no absolute phase angle. It's just like voltage -- it's always measured relative to something you pick as a reference.
But in EE, the AC sources are usually sinusoids and back when I first studied about phasors in Physics, they were introduced as Asin(wt + phi) with phi being the phase angle.
They were just saying that sin(wt+phi) has a phase angle of phi with respect to sin(wt).
It's ok to represent sinusoid waveforms with either sin() or cos(). When speaking of phase angle just pick a a form that represents a phase angle of 0 and stick to it.
