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current location:Mathematical operation > History of Inequality Computation > Answer
    Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 1.94 <(50sinx-39.2)/(1+cosx) <2.44 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities:
        1.94 < ( 50 * sin x - 39.2 ) / ( 1 + cos x )         (1)
         ( 50 * sin x - 39.2 ) / ( 1 + cos x ) <2.44         (2)
        From the definition field of divisor
         1 + cos x ≠ 0        (3 )

    From inequality(1):
         x < -16.634415 或  -11.562357 < x < -10.35123 或  -5.279172 < x < -4.068045 或  1.004013 < x < 2.215141 或  7.287198 < x < 8.498326 或  x > 13.570384
    From inequality(2):
         -16.641563 < x < -11.535248 或  -10.358378 < x < -5.252063 或  -4.075192 < x < 1.031122 或  2.207993 < x < 7.314308 或  8.491178 < x < 13.597493
    From inequality(3):
         x < -3926991/250000 或  -3926991/250000 < x < -4712389/500000 或  -4712389/500000 < x < -3141593/1000000 或  -3141593/1000000 < x < 3141593/1000000 或  3141593/1000000 < x < 4712389/500000 或  4712389/500000 < x < 15707963/1000000 或  x > 15707963/1000000

    From inequalities (1) and (2)
         -16.641563 < x < -16.634415 或  -11.562357 < x < -11.535248 或  -10.358378 < x < -10.35123 或  -5.279172 < x < -5.252063 或  -4.075192 < x < -4.068045 或  1.004013 < x < 1.031122 或  2.207993 < x < 2.215141 或  7.287198 < x < 7.314308 或  8.491178 < x < 8.498326 或  13.570384 < x < 13.597493     (4)
    From inequalities (3) and (4)
         -16.641563 < x < -16.634415 或  -11.562357 < x < -11.535248 或  -10.358378 < x < -10.35123 或  -5.279172 < x < -5.252063 或  -4.075192 < x < -4.068045 或  1.004013 < x < 1.031122 或  2.207993 < x < 2.215141 或  7.287198 < x < 7.314308 或  8.491178 < x < 8.498326 或  13.570384 < x < 13.597493     (5)

    The final solution set is :

         -16.641563 < x < -16.634415 或  -11.562357 < x < -11.535248 或  -10.358378 < x < -10.35123 或  -5.279172 < x < -5.252063 或  -4.075192 < x < -4.068045 或  1.004013 < x < 1.031122 或  2.207993 < x < 2.215141 或  7.287198 < x < 7.314308 或  8.491178 < x < 8.498326 或  13.570384 < x < 13.597493

    *Note: Radian.



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