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Math Help - [SOLVED] Sum and difference identities

  1. #1
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    [SOLVED] Sum and difference identities

    Q) if  sin \alpha =12/13 , \alpha is in the first quadrant ;  sin \beta =7/25 , \beta in the first quadrants.
    Find a)  sin (\alpha+\beta) b) cos(\alpha+\beta) c)the quadrant containing  (\alpha +\beta)
    Please answer in Steps..
    Thank you
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  2. #2
    Member arpitagarwal82's Avatar
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    \sin\alpha = 12/13 gives
    \cos\alpha = sqrt{1 - (12/13)^2}
    => \sin\alpha = 5/13

    Similarly \cos\beta = 24/25

    Now expand \sin (\alpha + \beta) and  \cos(\alpha + \beta) in terms of \sin\alpha, \cos\alpha and \sin\beta, \cos\beta
    After this replace the value and proceed.
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  3. #3
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    solve

    the soluation..............
    Attached Thumbnails Attached Thumbnails [SOLVED] Sum and difference identities-po20.jpg  
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  4. #4
    Member arpitagarwal82's Avatar
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    Hello ekledes
    Your solution is all right, excpet for c part.
    \alpha + \beta is in first qurdrant, but niot because 0  < \sin(\alpha + \beta) < 1, but because  0 < \cos(\alpha + \beta) < 1.
    Sine function is positive in both first and second quadrant. Its cos function which is negative in second quadrant. So here deciding factor is cos value not sin value
    Last edited by arpitagarwal82; February 25th 2009 at 05:57 AM.
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  5. #5
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    in deed iam choose this condition 0<sin(x+y)<1
    becouse the function cos is belong to the same interval
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