# 3 b) Show that the function given by f (x) = $\sin x$ isdecreasing in $\left ( \frac{\pi}{2},\pi \right )$

$f^{'}(x) = \cos x$
Since,  $\cos x < 0$  for each $x \ \epsilon \left ( \frac{\pi}{2},\pi \right )$
So, we have    $f^{'}(x) < 0$
Hence, f(x) = sin x is strictly decreasing in $\left ( \frac{\pi}{2},\pi \right )$