Knowing that $\sin x=\frac{2}{5}$ and $\frac{\pi}{2} \leq x \leq \pi$, Find the value $f$ or $\cot (x)$

Step 1 ：Given that \(\sin x = \frac{2}{5}\) and \(\frac{\pi}{2} \leq x \leq \pi\), we need to find \(\cot x = \frac{\cos x}{\sin x}\)

Step 2 ：Using the Pythagorean identity \(\sin^2 x + \cos^2 x = 1\), we find \(\cos x \approx -0.92\)

Step 3 ：Finally, we calculate \(\cot x = \frac{-0.92}{\frac{2}{5}} \approx -2.29\)

Step 4 ：\(\boxed{-2.29}\) is the value of \(\cot x\)