Sine and sines and sines and

Geometry Level 5

Consider the function from the positive integers to the reals \(f(n)=\sin 1^{\circ}+\sin 2^{\circ}+ \sin 3^{\circ}+\cdots+\sin n^{\circ}\). Find the maximum possible value of \(f(n)\) as \(n\) ranges over all positive integers. Leave your answer to the nearest integer.

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