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Homework Help: Exponential forms of cos and sin

  1. Nov 3, 2006 #1
    hi, my question is from Modern Engineering Mathematics by Glyn James

    pg 177 # 17a

    Using the exponential forms of cos(theta) and sin(theta) given in (3.11a, b), prove the following trigonometric identities:
    a) sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

    and 3.11a is:
    cos(x) = 0.5*[ e^(jx) + e^(-jx) ] where x= theta
    and 3.11b is:
    sin(x) = 0.5j*[ e^(jx) - e^(-jx) ] where x= theta

    i've gotten to the point where i have
    [ e^j(x+y) + e^j(x-y) -e^j(y-x) -e^-j(x + y) ] / 2j
     
  2. jcsd
  3. Nov 3, 2006 #2

    quasar987

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    3.11b should be

    sin(x) = 0.5*[ e^(jx) - e^(-jx) ]/j

    or

    sin(x) = -0.5j*[ e^(jx) - e^(-jx) ]

    What you want to do here is start with the expression 3.11b of sin(x+y), then use the property of the exponential that exp(x+y)=exp(x)exp(y) and then transform the exponentials back into sin and cos form. Then the real part of that is sin(x+y) (and the imaginary part equals 0).
     
  4. Nov 7, 2006 #3
    whoops i meant for the j to be on the bottom for 3.11b

    its like
    [1/(2j)][ e^(jx) - e^(-jx) ]
     
  5. Nov 7, 2006 #4
    weee i got it thanks for the help!
     
  6. Nov 8, 2006 #5

    HallsofIvy

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    Oh, those engineers and their jmagjnary numbers!
     
  7. Oct 21, 2008 #6
    hello my physics chums,
    hows your equations looking? I want somebody to love me.

    kevmyster
     
  8. Oct 21, 2008 #7
    Yes that's a pain in the ..., always confusion between i and j.
     
  9. Oct 21, 2008 #8
    In electrical engineering, i means electric current so imaginary numbers are written as j. I remember j was first introduced in the "Elementary linear circuit analysis" class and then all engineering classes use j instead of i. Yes, when reading mathematics or physics paper, I need to switch to i mode. And, mathematicians and physicists write Fourier transform in a confusing form:grumpy:
     
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