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 20^2+x^2-2*50*x*cos(180-arcsin((50*sin50)/x-50)) >(x+15)^2 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
20 ^ 2 + x ^ 2 - 2 * 50 * x * cos ( 180 - arcsin ( ( 50 * sin 50 ) / x - 50 ) ) > ( x + 15 ) ^ 2 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of arcsin
( 50 * sin 50 ) / x - 50 ≥ -1 (3 )
( 50 * sin 50 ) / x - 50 ≤ 1 (4 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
x < 0 或 x > 0
From inequality(3):
-0.267729 ≤ x ≤ 0
From inequality(4):
x ≤ -0.25723 或 x ≥ 0
From inequalities (1) and (2)
x < 0 或 x > 0 (5)
From inequalities (3) and (5)
-0.267729 ≤ x < 0 (6)
From inequalities (4) and (6)
-0.267729 ≤ x ≤ -0.25723 (7)
The final solution set is :
-0.267729 ≤ x ≤ -0.25723 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems !