(a) Transform (v(t)=100 cos left(377 t-30^{circ} ight)) to phasor form. Comment on whether (omega=) 377 appears in...

(a) Transform \(v(t)=100 \cos \left(377 t-30^{\circ}\right)\) to phasor form. Comment on whether \(\omega=\) 377 appears in your answer.

(b) Transform \(V=100 / 20^{\circ}\) to instantaneous form. Assume that \(\omega=377\).

(c) Add the two sinusoidal functions \(a(t)\) and \(b(t)\) of the same frequency given as follows: \(a(t)=\mathrm{A} \sqrt{2} \cos (\omega t+\alpha)\) and \(b(t)=\mathrm{B} \sqrt{2} \cos (\omega t+\beta)\). Use phasor methods and obtain the resultant \(c(t)\). Does the resultant have the same frequency?