Chapter 5 - Trigonometric Functions - Section 5.4 Graphs of the Sine and Cosine Functions* - 5.4 Assess Your Understanding - Page 433: 80

$-\frac{4}{\pi}$.

1. Given $f(x)=cos(2x)$, we have $f(0)=cos(0)=1$ and $f(\frac{\pi}{2}))=cos(2(\frac{\pi}{2}))=-1$. 2. We have the average rate of change as $R=\frac{f(\frac{\pi}{2})-f(0)}{\frac{\pi}{2}-1}=\frac{-2}{\frac{\pi}{2}}=-\frac{4}{\pi}$.