Chapter 5 - Trigonometric Functions - Section 5.4 Graphs of the Sine and Cosine Functions* - 5.4 Assess Your Understanding - Page 433: 78

$-\frac{2}{\pi}$.

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