The approximate value of cos31° is (take 1° = 0.0174)

$$\begin{gathered} \mathrm{x}=30 \mathrm{\delta x}=1^{\circ } =0.0174 \\ \mathrm{f}\left(\mathrm{x}\right) = \cos \mathrm{x} \\ \mathrm{f}(\mathrm{x}+\mathrm{\delta x})=\mathrm{f}\left(\mathrm{x}\right)+{\mathrm{f}}^1\left(\mathrm{x}\right)\mathrm{\delta x} \\ =\frac{\sqrt{3}}{2}+(-\sin \mathrm{x})\mathrm{\delta x} \\ =0.866-(0.5)(0.0174) \\ =0.8573 \end{gathered}$$