The function $ \sin(3\theta) + \cos(4\theta) $ is smooth and periodic. Its derivative is $ 3\cos(3\theta) - 4\sin(4\theta) $, which is non-zero almost everywhere, implying the function is strictly increasing or decreasing in intervals, but due to high frequency, we estimate number of times it crosses $ \pm1 $.

Fri, 01 May 2026 06:34:09 +0000

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