Answer
$-\frac{2}{\pi}$
Work Step by Step
Step 1. Given $f(x)=cos(x)$, we have $f(0)=cos(0)=1$ and $f(\frac{\pi}{2})=cos(\frac{\pi}{2})=0$
Step 2. The average rate of change over the given interval is $R=\frac{f(\frac{\pi}{2})-f(0)}{\frac{\pi}{2}-0}=\frac{0-1}{\frac{\pi}{2}}=-\frac{2}{\pi}$
