Answer
$\frac{\sqrt2}{\pi}$
Work Step by Step
The general formula for average rate of change from $x$ to $y$ is $\frac{f(y)-f(x)}{y-x}.$
Hence here:
$\frac{\sin(\frac{\frac{\pi}{2}}{2})-\sin(\frac{0}{2})}{\frac{\pi}{2}-0}
\\=\frac{\sin{\frac{\pi}{4}}-\sin{0}}{\frac{\pi}{2}}
\\=\frac{\frac{\sqrt2}{2}-0}{\frac{\pi}{2}}=\frac{\sqrt2}{\pi}.$
