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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality cosx/(sinx)^(1/2)+2(sinx)^(3/2)/cosx >= 2 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
cos x / ( sin x ) ^ ( 1 / 2 ) + 2 * ( sin x ) ^ ( 3 / 2 ) / cos x >= 2 (1)
From the definition field of divisor
sin x ≠ 0 (2 )
From inequality(1):
x ≤ -10.995574 或 -5856107/1000000 ≤ x ≤ -5856107/1000000 或 -5856107/1000000 ≤ x ≤ -4.712389 或 213539/500000 ≤ x ≤ 213539/500000 或 213539/500000 ≤ x ≤ 1.570796
From inequality(2):
x < -15.707963 或 -15.707963 < x < -12.566371 或 -12.566371 < x < -9.424778 或 -9.424778 < x < -6.283185 或 -6.283185 < x < -3.141593 或 -3.141593 < x < 0 或 0 < x < 3.141593 或 3.141593 < x < 6.283185 或 6.283185 < x < 9.424778 或 9.424778 < x < 12.566371 或 x > 12.566371
From inequalities (1) and (2)
x < -15.707963 或 -15.707963 < x < -12.566371 或 -12.566371 < x ≤ -10.995574 或 -5856107/1000000 ≤ x ≤ -5856107/1000000 或 -5856107/1000000 ≤ x ≤ -4.712389 或 213539/500000 ≤ x ≤ 213539/500000 或 213539/500000 ≤ x ≤ 1.570796 (3)
The final solution set is :
x < -15.707963 或 -15.707963 < x < -12.566371 或 -12.566371 < x ≤ -10.995574 或 -5856107/1000000 ≤ x ≤ -5856107/1000000 或 -5856107/1000000 ≤ x ≤ -4.712389 或 213539/500000 ≤ x ≤ 213539/500000 或 213539/500000 ≤ x ≤ 1.570796 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems !