Đáp án:
$S=\left\{-\dfrac{\pi}{18}+\arcsin\dfrac{3}{5}+k2\pi;\dfrac{17\pi}{18}-\arcsin\dfrac{3}{5}+k2\pi\,\bigg|\,k\in\mathbb Z\right\}$
Giải thích các bước giải:
$\sin(x+10^o)=\dfrac{3}{5}$
$⇔\sin\left(x+\dfrac{\pi}{18}\right)=\dfrac{3}{5}$
$⇔\left[ \begin{array}{l}x+\dfrac{\pi}{18}=\arcsin\dfrac{3}{5}+k2\pi\\x+\dfrac{\pi}{18}=\pi-\arcsin\dfrac{3}{5}+k2\pi\end{array} \right.\,\,(k\in\mathbb Z)$
$⇔\left[ \begin{array}{l}x=-\dfrac{\pi}{18}+\arcsin\dfrac{3}{5}+k2\pi\\x=\dfrac{17\pi}{18}-\arcsin\dfrac{3}{5}+k2\pi\end{array} \right.\,\,(k\in\mathbb Z)$
Vậy $S=\left\{-\dfrac{\pi}{18}+\arcsin\dfrac{3}{5}+k2\pi;\dfrac{17\pi}{18}-\arcsin\dfrac{3}{5}+k2\pi\,\bigg|\,k\in\mathbb Z\right\}$.
