1. The problem statement, all variables and given/known data v = 141.4sin(wt + 15) i = 14.14 cos(wt - 45) 2. Relevant equations Draw Phasors. P = VI cos(theta) Q = VI sin(theta) S = P + jQ theta is angle between V and I 3. The attempt at a solution V = 141.4sin(wt + 15) So Vrms = 141.4/1.414 sin(wt + 15) = 100 sin (wt + 15) I = 14.14 cos(wt - 45) Now cos (-theta) = cos(theta) So I = 14.14 cos (45-wt) So I = 14.14 sin(90-45 + wt) So I = 14.14 sin(45 + wt) I rms = 10sin(wt + 45) Now Vrms = 100sin(wt + 15) I rms = 10sin(wt + 45) I leads V by 30 degrees. theta = 30 degrees. P = VI cos(theta) = 100 * 10 * cos(30) = 866W Q = VI sin(theta) = 100 * 10 * sin(30) = 500VAR So S = P + jQ = 866 + j500 But in answer it is given S = 866 - j500 Where does the minus sign come from? I understand that it is leading power factor so it gives Q but mathematically sin(30) is positive value. So why should S have negative VAR?