9 If $2008=2^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{n}}$, where $a_{1}, a_{2}, \cdots, a_{n}$ are pairwise distinct non-negative integers, then the size relationship of $\sin \sum_{i=1}^{n} a_{i} 、 \cos \sum_{i=1}^{n} a_{i} 、 \tan \sum_{i=1}^{n} a_{i}$ is $\qquad$. (Given $\pi=3.141592 \cdots$)
9 Because
$$
2008=2^{10}+2^{9}+2^{8}+2^{7}+2^{6}+2^{4}+2^{3} \text {, }
$$

so $\sum_{i=1}^{n} \alpha_{i}=47$. Since $\pi=3.141592 \cdots$, we know $3.14$
47. $1, \frac{89}{6} \pi0 .
$$

Since $y=\cos x$ is a decreasing function on $\left[14 \pi+\frac{5 \pi}{6}, 14 \pi+\pi\right]$, and $y=\tan x$ is an increasing function on $[14 \pi+$ $\left.\frac{5 \pi}{6}, 14 \pi+\pi\right]$, we have
$$
\begin{array}{l}
\cos 47\tan \left(14 \pi+\frac{5 \pi}{6}\right)=-\frac{\sqrt{3}}{3} .
\end{array}
$$

Therefore, $\sin \sum_{i=1}^{n} \alpha_{i}>\tan \sum_{i=1}^{n} \alpha_{i}>\cos \sum_{i=1}^{n} \alpha_{i}$.