Вычислите sin a/2 и cos a/2, если cosa=1/8 и 3π/2<a<2π.

\[\cos a = \frac{1}{8};\ \ \ \ \]

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

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

\[\sin\frac{a}{2} = \sqrt{\frac{1 - \cos a}{2}} = \sqrt{\frac{1 - \frac{1}{8}}{2}} =\]

\[= \sqrt{\frac{7}{16}} = \left| \frac{\sqrt{7}}{4} \right| = - \frac{\sqrt{7}}{4}\]

\[\cos\frac{a}{2} = \sqrt{\frac{1 + \cos a}{2}} = \sqrt{\frac{1 + \frac{1}{8}}{2}} =\]

\[= \sqrt{\frac{9}{16}} = - \frac{3}{4}\]