SOLUTION: please help me answer the following question: "Two voltages: V1 = 6 cos(10t), V2 = 8 sin(10t) are inputs to a circuit. Determine an expression for the output voltage, v, if th

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: please help me answer the following question: "Two voltages: V1 = 6 cos(10t), V2 = 8 sin(10t) are inputs to a circuit. Determine an expression for the output voltage, v, if th      Log On

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Question 1115048: please help me answer the following question:
"Two voltages:
V1 = 6 cos(10t), V2 = 8 sin(10t)
are inputs to a circuit. Determine an expression for the output voltage, v, if this is given by:
V = V1 + V2 = A sin(10t + α)
i.e. determine the values of A and α, where α is in radians"

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
a*cos(x) + b*sin(x) = c * sin(x + p)
c = +sqrt%28a%5E2%2Bb%5E2%29+
p = phase shift = +tan%5E-1%28a%2Fb%29+
You have
a=6
b=8
(and x=10t which just gets carried along)
so you can plug in to find
+highlight%28V+=++V%5B1%5D+%2B+V%5B2%5D+=+10sin%2810t+%2B+36.8699%5Eo%29+%29+
——
To get the phase shift in radians: +36.8699+%2A+%28+pi%2F180+%29++=+0.6435+ radians