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Solution inequality：
Directly input the univariate inequality (that is, the inequality containing only one variable), set the angular unit (radian or angle) of the trigonometric function, and click the "Next" button to obtain the solution set of the inequality.
It supports mathematical functions (including trigonometric functions).
Directly input the univariate inequality (that is, the inequality containing only one variable), set the angular unit (radian or angle) of the trigonometric function, and click the "Next" button to obtain the solution set of the inequality.
It supports mathematical functions (including trigonometric functions).
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 <(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