#### Answer

$\Delta y\approx-0.007$

#### Work Step by Step

For small $\Delta x$, $\Delta y\approx dy$.
That is, $\Delta y\approx f'(a) dx$.
$f'(a)=-\sin a=-\sin \frac{\pi}{6}= -\frac{1}{2}$
$dx=0.014$
$\implies \Delta y\approx -\frac{1}{2}\times0.014=-0.007$