Question例 8 利用微分计算 $\sin 30^{\circ} 30^{\prime}$ 的近似值. 解 把 $30^{\circ} 30^{\prime}$ 化为弧度, 得 $$30^{\circ} 30^{\prime}=\frac{\pi}{6}+\frac{\pi}{360}$$

Studdy Solution
Calculate the numerical value.
$$\frac{1}{2} + \frac{\pi \sqrt{3}}{720} \approx 0.5 + \frac{3.14159 \cdot 1.73205}{720}$$ $$\approx 0.5 + 0.00755 \approx 0.50755$$
The approximate value of $\sin 30^{\circ} 30^{\prime}$ is $0.50755$.