We are given the equation;
[tex]y=\sin x[/tex]
Where we have
[tex]\begin{gathered} \sin \frac{\pi}{2}=1 \\ \text{AND} \\ \sin -(\frac{\pi}{2})=-1 \end{gathered}[/tex]
We can add 2pi and 4pi to -(pi/2);
[tex]\begin{gathered} 2\pi+(-\frac{\pi}{2}) \\ =\frac{4\pi-\pi}{2} \\ =\frac{3\pi}{2} \\ \text{Also;} \\ 4\pi+(-\frac{\pi}{2}) \\ =\frac{8\pi-\pi}{2} \\ =\frac{7\pi}{2} \end{gathered}[/tex]
In other words;
[tex]\sin (\frac{3\pi}{2})=\sin (\frac{7\pi}{2})=-1[/tex]
Therefore;
[tex]\frac{7\pi}{2}\text{ lies between 2}\pi\text{ and 4}\pi[/tex]
ANSWER:
[tex]\frac{7\pi}{2}[/tex]
