Đáp án:
7) \(\left[ \begin{array}{l}
x = - \dfrac{{55}}{3}^\circ + 120^\circ k\\
x = \dfrac{{215}}{3}^\circ + 120^\circ k
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
7)\sin \left( {3x + 10^\circ } \right) = - \dfrac{1}{{\sqrt 2 }}\\
\to \left[ \begin{array}{l}
3x + 10^\circ = - 45^\circ + 360^\circ k\\
3x + 10^\circ = 180 + 45^\circ + 360^\circ k
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = - \dfrac{{55}}{3}^\circ + 120^\circ k\\
x = \dfrac{{215}}{3}^\circ + 120^\circ k
\end{array} \right.\left( {k \in Z} \right)\\
10)\sin x = - \dfrac{6}{3} = - 2\left( {vô lý} \right)\\
Do:\sin x \in \left[ { - 1;1} \right]\\
\to x \in \emptyset \\
16)\cos x = \dfrac{1}{3}\\
Đặt:\dfrac{1}{3} = \cos a\\
\to \cos x = \cos a\\
\to x = \pm a + k2\pi \left( {k \in Z} \right)
\end{array}\)
