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Math Help - Find all solution of the following equation in the interval

  1. #1
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    Find all solution of the following equation in the interval

    Find all solution of the following equation in the interval [0,2)

    2sin^2 x = 2+ cos x
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  2. #2
    Junior Member mrmohamed's Avatar
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    Quote Originally Posted by Nessa214 View Post
    Find all solution of the following equation in the interval [0,2)

    2sin^2 x = 2+ cos x
    HI ALL
    Put sin^2x = 1 - cos^2x
    2 - 2 cos^2x= 2+ cosx
    2 cos^2x + cos x = 0
    cos x ( 2 cos x +1 ) =0
    cos x = 0 x = pi/2 , x = 3 pi / 2
    2 cos x + 1 =0 cos x = -1/2 x = 2 pi/3 , x = 4 pi / 3
    S.S = { pi/2 , 3pi/2 , 2 pi/3 , 4 pi/3 }
    mrmohamed
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  3. #3
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    Quote Originally Posted by mrmohamed View Post
    HI ALL
    Put sin^2x = 1 - cos^2x
    2 - 2 cos^2x= 2+ cosx
    2 cos^2x + cos x = 0
    cos x ( 2 cos x +1 ) =0
    cos x = 0 x = pi/2 , x = 3 pi / 2
    2 cos x + 1 =0 cos x = -1/2 x = 2 pi/3 , x = 4 pi / 3
    S.S = { pi/2 , 3pi/2 , 2 pi/3 , 4 pi/3 }
    mrmohamed


    thanks so much!
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