Question 52
Determine the largest positive integer $k$ for which exists a positive integer $n$ such that:
$$
\sin(n + 1) \lt \sin(n + 2) \lt \sin(n + 3) \lt \dots \lt \sin(n + k).
$$
$$
\sin(n + 1) \lt \sin(n + 2) \lt \sin(n + 3) \lt \dots \lt \sin(n + k).
$$