# Trigonometry (3)

Geometry Level 4

If $\large 2008=2^{a_1}+2^{a_2}+\cdots+2^{a_n}$ where $$a_1$$, $$a_2$$, $$\cdots$$, $$a_n$$ are distinct non-negative integers, let $x=\sin\sum_{i=1}^na_i$ $y=\cos\sum_{i=1}^na_i$ $z=\tan\sum_{i=1}^na_i$ Compare the sizes of $$x$$, $$y$$ and $$z$$.

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