\min |2\sin x + 3\cos x + 4| = \min (2\sin x + 3\cos x + 4) = 4 - \sqrt13 + 0? \quad \text{Wait — no: the minimum of the inner expression is $ 4 - \sqrt13 \approx 0.395 $, so the minimum of the absolute value is just its minimum value because it's positive. - Portal da Acústica