Вычислите sin a/2 и cos a/2, если cosa=1/18 и 3π/2<a<2π.

\[\cos a = \frac{1}{18};\ \ \ \]

\[\frac{3\pi}{2} < a < 2\pi \Longrightarrow \frac{3\pi}{4} < \frac{a}{2} < \pi \Longrightarrow\]

\[\Longrightarrow \sin\frac{a}{2} > 0;\ \cos\frac{a}{2} < 0\]

\[\sin\frac{a}{2} = \sqrt{\frac{1 - \cos a}{2}} = \sqrt{\frac{1 - \frac{1}{18}}{2}} =\]

\[= \sqrt{\frac{17}{36}} = \frac{\sqrt{17}}{6}\ \]

\[\cos\frac{a}{2} = \sqrt{\frac{1 + \cos a}{2}} = \sqrt{\frac{1 + \frac{1}{18}}{2}} =\]

\[= \sqrt{\frac{19}{36}} = \left| \frac{\sqrt{19}}{6} \right| = - \frac{\sqrt{19}}{6}\]