A Wave That Fills Every Window

Problem

Let $m$ be a positive integer and

f(x) = \sin\left(\frac{m}{5}x + \frac{\pi}{3}\right).

Suppose that for every integer $n$ ,

\{\, f(x) \mid n \le x \le n+1 \,\} = [-1, 1].

Find the smallest possible $m$ .

Answer

Solution

Difficulty	7/10
Topics	functions, trigonometry

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