516. Find approximately $\sin 31^{\circ}$.
Solution. We will find an approximate value of the function $\boldsymbol{y}=$ $=\sin x$ at $x=31^{\circ}$, based on its exact value at $x=30^{\circ}$. We have $\sin 30^{\circ}=0.5, d x \approx \Delta x=31^{\circ}-30^{\circ}=1^{\circ}$ (or in radians $d x=0.0175$).

Let's find $d y=\cos x d x$. Further, at $x=30^{\circ}, d x=0.0175$ we get $d y=$ $=\cos 30^{\circ} \cdot 0.0175=0.866 \cdot 0.0175=0.015$.

Thus, $\sin 31^{\circ} \approx \sin 30^{\circ}+d y=0.5+0.015=0.515$.

517-520. Calculate the approximate values of the following functions: