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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 1.94 <(50sin(2x)-39.2)/(1+cos(2x)) <2.44 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
1.94 < ( 50 * sin ( 2 * x ) - 39.2 ) / ( 1 + cos ( 2 * x ) ) (1)
( 50 * sin ( 2 * x ) - 39.2 ) / ( 1 + cos ( 2 * x ) ) <2.44 (2)
From the definition field of divisor
1 + cos ( 2 * x ) ≠ 0 (3 )
From inequality(1):
x < -8.317208 或 -5.781179 < x < -5.175615 或 -2.639586 < x < -2.034022 或 0.502007 < x < 1.10757 或 3.643599 < x < 4.249163 或 x > 6.785192
From inequality(2):
-8.320781 < x < -5.767624 或 -5.179189 < x < -2.626032 或 -2.037596 < x < 0.515561 或 1.103997 < x < 3.657154 或 4.245589 < x < 6.798746
From inequality(3):
x < -3926991/500000 或 -3926991/500000 < x < -4712389/1000000 或 -4712389/1000000 < x < -1570797/1000000 或 -1570797/1000000 < x < 1570797/1000000 或 1570797/1000000 < x < 4712389/1000000 或 4712389/1000000 < x < 3926991/500000 或 x > 3926991/500000
From inequalities (1) and (2)
-8.320781 < x < -8.317208 或 -5.781179 < x < -5.767624 或 -5.179189 < x < -5.175615 或 -2.639586 < x < -2.626032 或 -2.037596 < x < -2.034022 或 0.502007 < x < 0.515561 或 1.103997 < x < 1.10757 或 3.643599 < x < 3.657154 或 4.245589 < x < 4.249163 或 6.785192 < x < 6.798746 (4)
From inequalities (3) and (4)
-8.320781 < x < -8.317208 或 -5.781179 < x < -5.767624 或 -5.179189 < x < -5.175615 或 -2.639586 < x < -2.626032 或 -2.037596 < x < -2.034022 或 0.502007 < x < 0.515561 或 1.103997 < x < 1.10757 或 3.643599 < x < 3.657154 或 4.245589 < x < 4.249163 或 6.785192 < x < 6.798746 (5)
The final solution set is :
-8.320781 < x < -8.317208 或 -5.781179 < x < -5.767624 或 -5.179189 < x < -5.175615 或 -2.639586 < x < -2.626032 或 -2.037596 < x < -2.034022 或 0.502007 < x < 0.515561 或 1.103997 < x < 1.10757 或 3.643599 < x < 3.657154 或 4.245589 < x < 4.249163 或 6.785192 < x < 6.798746 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems !