Infimum and supremum of $\{x\in[-1,4]\mid\sin x>0\}$ Let $S=\{X\in[-1,4]\mid\sin(x)&gt;0\}$. Which of the following is true?
  $\inf(S)&lt;0$,
  $\sup(S)$ does not exist,
  $\sup(S)=π$,
  $\inf(S)=\dfracπ2$.
  


I was trying to get the infimum and supremum of the set, but I am not able solve it. Please help.
Since sin(x)>0, x can take values only between 0 and π(3.14) as you can see in the graph of sin function. So the set S = {x€[-1,4] | sin(x)>0} will be reduce to S={x€(0,π(3.14)) | sin(x)>0} . Sup(S) is not 4. Therefore, The correct answer is Sup(S) = π.
Since sin(x)>0, x can take values only between 0 and π(3.14) as you can see in the graph of sin function. So the set S = {x€[-1,4] | sin(x)>0} will be reduce to S={x€(0,π(3.14)) | sin(x)>0} . Sup(S) is not 4. Therefore, The correct answer is Sup(S) = π.