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2017 preRMO p11, f(x) = sin (x/3)+ cos (3x/10), f(n\pi +x)= f(x)

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August 9, 2019
trigonometryperiodic functionminimum

Problem Statement

Let f(x)=sin⁡x3+cos⁡3x10f(x) = \sin \frac{x}{3}+ \cos \frac{3x}{10} for all real xx. Find the least natural number nn such that f(nπ+x)=f(x)f(n\pi + x)= f(x) for all real xx.
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