SOLUTION: please help me answer this question: "Two voltages: V1 = 3 cos(5t), V2 = 4 sin(5t) are inputs to a circuit. Determine an expression for the output voltage, v, if this is given

Question 1115565: please help me answer this question:
"Two voltages:
V1 = 3 cos(5t), V2 = 4 sin(5t)
are inputs to a circuit. Determine an expression for the output voltage, v, if this is given by:
V = V1 + V2 = A sin(5t + α)
i.e. determine the values of A and α, where α is in radians"
Answer by ikleyn(52851) (Show Source): You can put this solution on YOUR website!
.

V1 + V2 = 3*cos(5t) + 4*sin(5t) =     (1)


          Since  =  = 1,  there is (= does exist) the angle "a" in QI such that  sin(a) = ,  cos(a) = .

          With these identities, we can continue  (1) in this way:




V1 + V2 = 3*cos(5t) + 4*sin(5t) =  = 5*(cos(5t)*sin(a) + sin(5t)*cos(a))     (2)

         Now apply the sine addition formula, and you can continue (2) in this way  




V1 + V2 =  =  = 5*(cos(5t)*sin(a) + sin(5t)*cos(a)) = 5*sin(5t+a).



It is just what the problem wants of you with  A = 5  and   = a =  = .

Solved.

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