I have to find how many microseconds the load voltage is out of phase with the source voltage.

I have the vs = 480sqrt(2)cos(120pi*t+0deg)
and vl 694.25cos(120pi*t+1.01deg)

Would solving for t inside the cosine's give me the time out of phase?

ie. t1 = -0deg/120pi = 0
t2 = -1.01deg/120pi = -2.68mS ?

or am i approaching this completely wrong?

thanks for reading !

 

At 60 Hz, one cycle takes 16.67 ms. That is 46.3 us/degree.

 

Firstly, cos(2.pi.t) corresponds to a freqency of 1Hz, or period of 1s.
Therefore, cos(120.pi.t) is 60 times greater in frequency, with a period of 1/60s.
1.01 degrees represents 1.01/360 of a cycle's period.
So, the output leads the input by 1.01 / (360 * 60) s.