document.write( "Question 1115565: please help me answer this question:\r
\n" ); document.write( "\n" ); document.write( "\"Two voltages:
\n" ); document.write( "V1 = 3 cos(5t), V2 = 4 sin(5t)
\n" ); document.write( "are inputs to a circuit. Determine an expression for the output voltage, v, if this is given by:
\n" ); document.write( "V = V1 + V2 = A sin(5t + α)
\n" ); document.write( "i.e. determine the values of A and α, where α is in radians\" \n" ); document.write( "

Algebra.Com's Answer #730401 by ikleyn(52852) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "V1 + V2 = 3*cos(5t) + 4*sin(5t) =     (1)\r\n" );
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document.write( "          Since  =  = 1,  there is (= does exist) the angle \"a\" in QI such that  sin(a) = ,  cos(a) = .\r\n" );
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document.write( "          With these identities, we can continue  (1) in this way:\r\n" );
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document.write( "V1 + V2 = 3*cos(5t) + 4*sin(5t) =  = 5*(cos(5t)*sin(a) + sin(5t)*cos(a))     (2)\r\n" );
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document.write( "         Now apply the sine addition formula, and you can continue (2) in this way  \r\n" );
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document.write( "V1 + V2 =  =  = 5*(cos(5t)*sin(a) + sin(5t)*cos(a)) = 5*sin(5t+a).\r\n" );
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document.write( "It is just what the problem wants of you with  A = 5  and   = a =  = .\r\n" );
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