Đáp án:
$1-B$
$2-A$
$3-B$
$4-A$
$5-B$
Giải thích các bước giải:
Câu 1:
$sinx=\dfrac{1}{2}$
$↔ sinx=sin\dfrac{\pi}{6}$
$↔ \left[ \begin{array}{l}x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{5\pi}{6}+k2\pi\end{array} \right.$ $(k∈\mathbb{Z})$
Câu 2:
$cosx=0$
$↔ x=\dfrac{\pi}{2}+k\pi$ $(k∈\mathbb{Z})$
Câu 3:
$tanx=-\dfrac{\sqrt[]{3}}{3}$
$↔ tanx=tan\Bigg(-\dfrac{\pi}{6}\Bigg)$
$↔ x=-\dfrac{\pi}{6}+k\pi$ $(k∈\mathbb{Z})$
Câu 4:
$sin3x=sinx$
$↔ \left[ \begin{array}{l}3x=x+k2\pi\\3x=\pi-x+k2\pi\end{array} \right.$
$↔ \left[ \begin{array}{l}x=k\pi\\x=\dfrac{\pi}{4}+k\dfrac{\pi}{2}\end{array} \right.$ $(k∈\mathbb{Z})$
Câu 5:
$sin\Bigg(4x-\dfrac{\pi}{3}\Bigg)=\dfrac{1}{2}$
$↔ sin\Bigg(4x-\dfrac{\pi}{3}\Bigg)=sin\dfrac{\pi}{6}$
$↔ \left[ \begin{array}{l}4x-\dfrac{\pi}{3}=\dfrac{\pi}{6}+k2\pi\\4x-\dfrac{\pi}{3}=\dfrac{5\pi}{6}+k2\pi\end{array} \right.$
$↔ \left[ \begin{array}{l}x=\dfrac{\pi}{8}+k\dfrac{\pi}{2}\\x=\dfrac{7\pi}{24}+k\dfrac{\pi}{2}\end{array} \right.$ $(k∈\mathbb{Z})$
Câu 6:
$cotx=\sqrt[]{3}$
$↔ cotx=cot\dfrac{\pi}{6}$
$↔ x=\dfrac{\pi}{6}+k\pi$ $(k∈\mathbb{Z})$
