Answer
$\frac{-4}{\pi}$
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:
$\frac{\cos(2\cdot\frac{\pi}{2})-\cos(2\cdot 0)}{\frac{\pi}{2}-0}
\\=\frac{\cos{\pi}-\cos{0}}{\frac{\pi}{2}}
\\=\frac{-1-1}{\frac{\pi}{2}}
\\=\frac{-4}{\pi}$
