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Assignment:Find the solution set of inequality ln(-(sinx+lnx+e3)/cosx) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality：
ln ( -( sin x + ln x + e 3 ) / cos x ) >0 (1)
From the definition field of ln
x > 0 (2 )
From the definition field of ln
-( sin x + ln x + e 3 ) / cos x > 0 (3 )
From inequality(1)：
1.570796 < x < 7.853982 或 7.853982 < x < 14.137167 或 14.137167 < x < 20.420352 或 20.420352 < x < 26.703538 或 26.703538 < x < 32.986723 或 32.986723 < x < 39.269908 或 39.269908 < x < 45.553093 或 45.553093 < x < 51.836279 或 51.836279 < x < 58.119464 或 x ＞ 58.119464
From inequality(2)：
x ＞ 0
From inequality(3)：
x < 0 或 1.570796 < x < 4.712389 或 7.853982 < x < 10.995574 或 14.137167 < x < 17.27876 或 20.420352 < x < 23.561945 或 x ＞ 26.703538
From inequalities (1) and (2)
1.570796 < x < 7.853982 或 7.853982 < x < 14.137167 或 14.137167 < x < 20.420352 或 20.420352 < x < 26.703538 或 26.703538 < x < 32.986723 或 32.986723 < x < 39.269908 或 39.269908 < x < 45.553093 或 45.553093 < x < 51.836279 或 51.836279 < x < 58.119464 或 x ＞ 58.119464 (4)
From inequalities (3) and (4)
1.570796 < x < 4.712389 或 或 7.853982 < x < 10.995574 或 1.570796 < x < 7.853982 或 14.137167 < x < 17.27876 或 7.853982 < x < 14.137167 或 20.420352 < x < 23.561945 或 26.703538 < x < 32.986723 或 32.986723 < x < 39.269908 或 39.269908 < x < 45.553093 或 45.553093 < x < 51.836279 或 51.836279 < x < 58.119464 或 x ＞ 58.119464 (5)
The final solution set is :
1.570796 < x < 4.712389 或 或 7.853982 < x < 10.995574 或 1.570796 < x < 7.853982 或 14.137167 < x < 17.27876 或 7.853982 < x < 14.137167 或 20.420352 < x < 23.561945 或 26.703538 < x < 32.986723 或 32.986723 < x < 39.269908 或 39.269908 < x < 45.553093 或 45.553093 < x < 51.836279 或 51.836279 < x < 58.119464 或 x ＞ 58.119464 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems ！
