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Can we get 2010 by trigonometric functions applied on 1?

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February 9, 2011
functiontrigonometryalgebra unsolvedalgebra

Problem Statement

Consider a composition of functions sin⁡,cos⁡,tan⁡,cot⁡,arcsin⁡,arccos⁡,arctan⁡,arccos⁡\sin, \cos, \tan, \cot, \arcsin, \arccos, \arctan, \arccos, applied to the number 11. Each function may be applied arbitrarily many times and in any order. (ex: sin⁡cos⁡arcsin⁡cos⁡sin⁡⋯1\sin \cos \arcsin \cos \sin\cdots 1). Can one obtain the number 20102010 in this way?
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