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Math Help - pre-calc

  1. #1
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    pre-calc

    got it thanks
    Last edited by sksksk; November 19th 2007 at 07:21 PM.
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  2. #2
    Senior Member Peritus's Avatar
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    1. let's convert the angle to degrees pi/8 -> 45/2
    now use the formula for double angle -->
    cos(2*theta) = 2*[cos(theta/2)]^2 - 1
    it's well known that cos(45) = 1/sqrt(2)

    thus we get--> cos(45) = 2*[cos(45/2)]^2 - 1

    <=> cos(45/2) = sqrt[0.5*(cos(45)+1)] = sqrt[(1+sqrt(2))/(2*sqrt(2))]

    2. 2*cos(theta) = 1

    <=> theta = arccos(0.5) + 2*pi*k = pi/3 + 2*pi*k
    and also (5/3)*pi + 2*pi*k
    where k = 0,-1,1,2,-2,....

    3. simple enough to me
    4. -1-i = sqrt(2)e^(j7*pi/4)

    thus (-1-i)^4/3 = [2^(2/3)]e(j*7*pi/3) = use Euler identity...

    5. convert to polar form as in the previous section then convert back to Cartesian...
    Last edited by Peritus; November 19th 2007 at 02:36 PM.
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