依 \display style f(x):=\frac{\sin x}{x} 的單調減性，有 \display style f\left(\frac{1}{3}\right)> f\left(\frac{\pi}{6}\right), 於是 \display style\sin \frac{1}{3}> \frac{1}{3}\cdot\frac{\sin \frac{\pi}{6}}{\frac{\pi}{6}}=\frac{1}{\pi}.
依 \display style f(x):=\frac{\sin x}{x} 的單調減性，有 \display style f\left(\frac{1}{3}\right)> f\left(\frac{\pi}{6}\right), 於是 \display style\sin \frac{1}{3}> \frac{1}{3}\cdot\frac{\sin \frac{\pi}{6}}{\frac{\pi}{6}}=\frac{1}{\pi}.
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