Phương trình sin x = sin 2pi/ 3 có nghiệm là:

11/41

Phương trình \(\sin x = \sin \frac{{2\pi }}{3}\) có nghiệm là:

\(\left[ {\begin{array}{*{20}{l}}{x = \frac{{2\pi }}{3} + k2\pi }\\{x = - \frac{{2\pi }}{3} + k2\pi }\end{array}\,\,\,\left( {k \in \mathbb{Z}} \right)} \right..\)

\(\left[ {\begin{array}{*{20}{l}}{x = \frac{{2\pi }}{3} + k\pi }\\{x = \frac{\pi }{3} + k\pi }\end{array}\,\,\,\left( {k \in \mathbb{Z}} \right)} \right.\).

\(\left[ {\begin{array}{*{20}{l}}{x = \frac{\pi }{3} + k\pi }\\{x = - \frac{\pi }{3} + k\pi }\end{array}\,\,\,\,\left( {k \in \mathbb{Z}} \right)} \right..\)

\(\left[ {\begin{array}{*{20}{l}}{x = \frac{{2\pi }}{3} + k2\pi }\\{x = \frac{\pi }{3} + k2\pi }\end{array}\,\,\,\left( {k \in \mathbb{Z}} \right)} \right..\)

Giải thích

Chọn D

Ta có:\(\sin x = \sin \frac{{2\pi }}{3} \Leftrightarrow \left[ {\begin{array}{*{20}{l}}{x = \frac{{2\pi }}{3} + k2\pi }\\{x = \frac{\pi }{3} + k2\pi }\end{array}\,\,\,\left( {k \in \mathbb{Z}} \right)} \right..\)