Mister Exam

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pi/2>arcsin(x) inequation

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pi          
-- > asin(x)
2

\frac{\pi}{2} > \operatorname{asin}{\left(x \right)}

pi/2 > asin(x)

Detail solution

Given the inequality:

\frac{\pi}{2} > \operatorname{asin}{\left(x \right)}

To solve this inequality, we must first solve the corresponding equation:

\frac{\pi}{2} = \operatorname{asin}{\left(x \right)}

Solve:

x_{1} = 1

x_{1} = 1

This roots

x_{1} = 1

is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:

x_{0} < x_{1}

For example, let's take the point

x_{0} = x_{1} - \frac{1}{10}

- \frac{1}{10} + 1

\frac{9}{10}

substitute to the expression

\frac{\pi}{2} > \operatorname{asin}{\left(x \right)}

\frac{\pi}{2} > \operatorname{asin}{\left(\frac{9}{10} \right)}

pi             
-- > asin(9/10)
2

the solution of our inequality is:

x < 1

 _____          
      \    
-------ο-------
       x1

Solving inequality on a graph

Rapid solution [src]

And(-oo < x, x < 1)

-\infty < x \wedge x < 1

(-oo < x)∧(x < 1)

Rapid solution 2 [src]

(-oo, 1)

x\ in\ \left(-\infty, 1\right)

x in Interval.open(-oo, 1)