Minimal natural solution of inequality. Help.

deadmoon

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I need to find the minimal natural solution (answer) of this inequality?
Where should I start?
 

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Can you explain why are you using '=' in inequality?
Or should I solve these: sin(x) < 1/√2 and sin(x) < -1/√2 ??
But then, I think, there wouldn't be any natural solutions.. or am I wrong?
 
Can you explain why are you using '=' in inequality?
Or should I solve these: sin(x) < 1/√2 and sin(x) < -1/√2 ??
But then, I think, there wouldn't be any natural solutions.. or am I wrong?
Because, for continuous functions, like sine, places where they are "equal" separate "<" from ">". Here, since this is absolute value, \(\displaystyle |sin(x)|
< \sqrt{2}/2\) we have 2/2<x<2/2\displaystyle -\sqrt{2}/2< x< \sqrt{2}/2.
 
Because, for continuous functions, like sine, places where they are "equal" separate "<" from ">". Here, since this is absolute value, \(\displaystyle |sin(x)|
< \sqrt{2}/2\) we have 2/2<x<2/2\displaystyle -\sqrt{2}/2< x< \sqrt{2}/2.


I think there is surely a typo there:
sin(x)<2/2\displaystyle |sin(x)|< \sqrt{2}/2 we have 2/2<sin(x)<2/2\displaystyle -\sqrt{2}/2< \sin(x)< \sqrt{2}/2
 
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