Đáp án:
b) \(\tan a = - \dfrac{{\sqrt {17} }}{8}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)Do:\dfrac{{3\pi }}{2} < a < 2\pi \\
\to \sin a < 0\\
Có:\cos a = \dfrac{1}{5}\\
\to {\cos ^2}a + {\sin ^2}a = 1\\
\to \dfrac{1}{{25}} + {\sin ^2}a = 1\\
\to {\sin ^2}a = \dfrac{{24}}{{25}}\\
\to \left[ \begin{array}{l}
\sin a = \dfrac{{2\sqrt 6 }}{5}\left( l \right)\\
\sin a = - \dfrac{{2\sqrt 6 }}{5}
\end{array} \right.\\
\to \tan a = \dfrac{{\sin a}}{{\cos a}} = \dfrac{{2\sqrt 6 }}{5}:\dfrac{1}{5} = 2\sqrt 6 \\
\to \cot a = \dfrac{1}{{2\sqrt 6 }}\\
c)Do: - \dfrac{\pi }{2} < a < 0\\
\to \cos a > 0\\
Có:\sin a = - \dfrac{{\sqrt {17} }}{9}\\
\to {\cos ^2}a + {\sin ^2}a = 1\\
\to {\cos ^2}a + \dfrac{{17}}{{81}} = 1\\
\to {\cos ^2}a = \dfrac{{64}}{{81}}\\
\to \cos a = \dfrac{8}{9}\\
\to \tan a = - \dfrac{{\sqrt {17} }}{8}\\
\to \cot a = - \dfrac{8}{{\sqrt {17} }}
\end{array}\)
