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Homework Help: Could someone provide additional steps to get to the answer?

  1. Nov 11, 2015 #1
    1. The problem statement, all variables and given/known data
    determine A and φ: f(x)=Acos(2t+φ)=4cos(2t+1/4π)+5sin(2t)

    2. Relevant equations
    the answer has to be in the form of Aeφi

    3. The attempt at a solution
    for working towards the answer, the tekst states:


    I fail to see how they get 5e-1/2πi out of 5sin(2t). Also, how they reform it to -5i and how they go from 4e1/4πi to 2√2+2√2i

    from then, I guess its 2√2+(2√2-5)i=3,57e-0,65i, but it's the middle part that confuses me
  2. jcsd
  3. Nov 11, 2015 #2


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    Homework Helper

    You have to write all terms as cosines. sin(2t) is the cosine of what angle? Think of the definition of sine and cosine in a right triangle.
  4. Nov 11, 2015 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Why don't you use the trigonometric addition laws to write both sides of the equation as constant-coefficient linear combinations of ##\cos(2t)## and ##\sin(2t)##?
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