QPaperGen

We are given:
\(f(x) = \sin x \Rightarrow f'(x) = \cos x\)
\[\]

In the interval \(x \in \left(0,\dfrac{\pi}{2}\right)\), we have \(\cos x > 0 \Rightarrow f'(x) > 0\)
\(\Rightarrow f(x)\) is strictly increasing in \(\left(0,\dfrac{\pi}{2}\right)\)
\[\]

In the interval \(x \in \left(\dfrac{\pi}{2},\pi\right)\), we have \(\cos x < 0 \Rightarrow f'(x) < 0\)
\(\Rightarrow f(x)\) is strictly decreasing in \(\left(\dfrac{\pi}{2},\pi\right)\)
\[\]

Since \(f\) increases in part of the interval and decreases in another,
\(f\) is neither increasing nor decreasing in the entire interval \((0,\pi)\).