[Math] Infimum and supremum of $\{x\in[-1,4]\mid\sin x>0\}$

Question

Let $S=\{X\in[-1,4]\mid\sin(x)>0\}$. Which of the following is true?

1. $\inf(S)<0$,
2. $\sup(S)$ does not exist,
3. $\sup(S)=π$,
4. $\inf(S)=\dfracπ2$.

I was trying to get the infimum and supremum of the set, but I am not able solve it. Please help.

Answer 1

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.