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SMO 2016 Open Round 1 Question 12

SMO · SMO 2016 Open Round 1

Question 12

In this paper, let $[x]$ denote the greatest integer not exceeding x. For examples, $[5]=5$, $[2.8]=2$, and $[-2.3]=-3$.

Given that $z=\lim_{\theta\to 0}\frac{\sin\theta^\circ}{\theta}$, find $\left[\frac{360 z}{\pi}\right]$.