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Assignment:Find the solution set of inequality 0 ≤arcsin(2x-1) ≤2/π .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
0 ≤ arcsin ( 2 * x - 1 ) (1)
arcsin ( 2 * x - 1 ) ≤2 / π (2)
From the definition field of arcsin
2 * x - 1 ≥ -1 (3 )
2 * x - 1 ≤ 1 (4 )
From inequality(1):
x ≥ 1/2
From inequality(2):
x ≤ 0.79724
From inequality(3):
x ≥ 0
From inequality(4):
x ≤ 1
From inequalities (1) and (2)
1/2 ≤ x ≤ 0.79724 (5)
From inequalities (3) and (5)
1/2 ≤ x ≤ 0.79724 (6)
From inequalities (4) and (6)
1/2 ≤ x ≤ 0.79724 (7)
The final solution set is :
1/2 ≤ x ≤ 0.79724Your problem has not been solved here? Please take a look at the hot problems !