Phương trình \(\cos x = - \frac{1}{2}\) có các nghiệm là:

A. \(\left[ \begin{array}{l}x = \frac{\pi }{3} + k2\pi \\x = - \frac{\pi }{3} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\).

B. \(\left[ \begin{array}{l}x = \frac{{5\pi }}{6} + k2\pi \\x = - \frac{{5\pi }}{6} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\).

C. \(\left[ \begin{array}{l}x = \frac{{2\pi }}{3} + k2\pi \\x = \frac{\pi }{3} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\).

D. \(\left[ \begin{array}{l}x = \frac{{2\pi }}{3} + k2\pi \\x = - \frac{{2\pi }}{3} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\).

Đáp án đúng là: D

Ta có: \(\cos x = - \frac{1}{2}\)\( \Leftrightarrow \cos x = \cos \frac{{2\pi }}{3}\)\( \Leftrightarrow \left[ \begin{array}{l}x = \frac{{2\pi }}{3} + k2\pi \\x = - \frac{{2\pi }}{3} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\).