Finding Expression for V1 + V2 Waveforms

[zak8000]

say i have the following waveforms

V1=10cos(wt)
V2=20sin(wt)

and i am told to find an analytic expression for the resulting voltage waveform

fristly i found the V1+V2 add the two phasors at t= 0 to get 22.4 and then i found theta which is 26.5 (tan^-1(10/20)) but now I am confused will the expression be:

V=22.4sin(wt+26.5)

or

V=22.4cos(wt+26.5)

 

[mathman]

You can use the cos(a+b) and sin(a+b) expansions and see which one gives you the original V1 and V2.

 

[Born2bwire]

At t=0 it is trivial to calculate the result of the original voltages.

At t=0, V = 10. So which of the two expressions for V that you have satisfy this relationship?