Nghiệm \(x = \dfrac{{2\pi }}{3}\) là của phương trình nào dưới đây?
\(\sin x = - \dfrac{1}{2}\)
\(\cot x = - \dfrac{{\sqrt 3 }}{3}\)
\(\tan x = \sqrt 3 \)
\(\cos x = - \dfrac{1}{2}\)
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
- Đáp án A: \(\sin x = - \dfrac{1}{2} = \sin \left( { - \dfrac{\pi }{6}} \right)\) \( \Leftrightarrow \left[ \begin{array}{l}x = - \dfrac{\pi }{6} + k2\pi \\x = \dfrac{{7\pi }}{6} + k2\pi \end{array} \right.\,\,\left( {k \in \mathbb{Z}} \right)\) (loại).
- Đáp án B: \(\cot x = - \dfrac{{\sqrt 3 }}{3} = \cot \left( { - \dfrac{\pi }{3}} \right)\) \( \Leftrightarrow x = - \dfrac{\pi }{3} + k2\pi \,\,\left( {k \in \mathbb{Z}} \right)\) (loại).
- Đáp án C: \(\tan x = \sqrt 3 = \tan \dfrac{\pi }{3}\) \( \Leftrightarrow x = \dfrac{\pi }{3} + k2\pi \,\,\left( {k \in \mathbb{Z}} \right)\) (loại).
- Đáp án D: \(\cos x = - \dfrac{1}{2} = \cos \dfrac{{2\pi }}{3}\) \( \Leftrightarrow x = \pm \dfrac{{2\pi }}{3} + k2\pi \,\,\left( {k \in \mathbb{Z}} \right)\) (thỏa mãn).
Đáp án là D.
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