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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.Your problem has not been solved here? Please take a look at the hot problems !