Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
4,\\
0 < x < \dfrac{\pi }{2} \Rightarrow \left\{ \begin{array}{l}
\sin x > 0\\
\cos x > 0
\end{array} \right.\\
\tan x = \dfrac{1}{3} \Rightarrow \left\{ \begin{array}{l}
\cot x = \dfrac{1}{{\tan x}} = 3\\
\dfrac{{\sin x}}{{\cos x}} = \dfrac{1}{3} \Leftrightarrow \cos x = 3\sin x
\end{array} \right.\\
{\sin ^2}x + {\cos ^2}x = 1\\
\Leftrightarrow {\sin ^2}x + {\left( {3\sin x} \right)^2} = 1\\
\Leftrightarrow {\sin ^2}x = \dfrac{1}{{10}}\\
\sin x > 0 \Rightarrow \sin x = \dfrac{1}{{\sqrt {10} }}\\
4,\\
\pi < x < \dfrac{{3\pi }}{2} \Rightarrow \left\{ \begin{array}{l}
\sin x < 0\\
\cos x < 0
\end{array} \right.\\
{\sin ^2}x + {\cos ^2}x = 1\\
\cos x < 0 \Rightarrow \cos x = - \sqrt {1 - {{\sin }^2}x} = - \dfrac{{2\sqrt 2 }}{3}\\
\tan x = \dfrac{{\sin x}}{{\cos x}} = \dfrac{1}{{2\sqrt 2 }}
\end{array}\)
