Understanding Phase Differences in Sinusoidal Waveforms

[pyroknife]

This is just an example
X=-20cos(t)
y=cos(t-45deg)

X has to be positive so X=-20cos(t±180deg)
I know you want the angle ^ to be the smallest magnitude, but for this case both would give you a magnitude of 180 deg.
So which one would you pick X=20cos(t-180deg) or X=20cos(t+180deg)?
This would change the answer of whether X or Y was leading.

Someone told me you should pick the angle that makes a phase difference that is <180deg.
So in this case it would be X=20cos(t-180deg) since that would give a phase difference of 135 degree compared to the 180+45=225deg phase difference if we picked the positive.

Is that right?

 

[azizlwl]

X=-20cos(t)
y=sin(t-45deg)

Z=Sin(t)
X=20cos(t)=20Sin(t+90deg)
Y=Sin(t-45deg)

X leading normal sine wave Z by 90 degree
Y lagging normal sine wave Z by 45 degree.

X leading Y by 135 degree.
http://img855.imageshack.us/img855/5074/leadlag.jpg