3. Вычислить \(\cos a\), \(\tan a\), \(\cot a\), если \(\sin a=-\frac25\) и \(\pi<a<\frac{3\pi}{2}\).

Так как \(\pi

По основному тригонометрическому тождеству:

\(\cos a=-\sqrt{1-\sin^2a}=-\sqrt{1-\frac{4}{25}}=-\sqrt{\frac{21}{25}}=-\frac{\sqrt{21}}{5}\).

\(\tan a=\frac{\sin a}{\cos a}=\frac{-\frac25}{-\frac{\sqrt{21}}5}=\frac{2}{\sqrt{21}}=\frac{2\sqrt{21}}{21}\).

\(\cot a=\frac{1}{\tan a}=\frac{\sqrt{21}}2\).

Ответ: \(\cos a=-\frac{\sqrt{21}}5\), \(\tan a=\frac{2\sqrt{21}}{21}\), \(\cot a=\frac{\sqrt{21}}2\).