Question

Найдите корень уравнения sin п(x-1)/3=корень из 3/2

Answer 1

$2+6n,~n\in\mathbb {Z}; 3+6k,~k\in\mathbb {Z}.$

Объяснение:

$sin \frac{\pi (x-1)}{3} =\frac{\sqrt{3} }{2} \Leftrightarrow\left [ \begin{array}{lcl} {{\frac{\pi (x-1)}{3} =\frac{\pi }{3} +2\pi n, ~n\in\mathbb {Z},} \\ {\frac{\pi( x-1)}{3} =\frac{2 \pi }{3} +2\pi k, ~k\in\mathbb {Z}};} \end{array} \right.\Leftrightarrow$

$\Leftrightarrow \left [ \begin{array}{lcl} {{\pi (x-1) =\pi+6\pi n, ~n\in\mathbb {Z}} \\ {\pi (x-1)=2\pi +6\pi k,~k\in\mathbb {Z}}} \end{array} \right.\Leftrightarrow \left [ \begin{array}{lcl} {{x-1=1+6n,~n\in\mathbb {Z}} \\ {x-1=2+6k,~k\in\mathbb {Z}}} \Leftrightarrow\end{array} \right.$

$\Leftrightarrow \left [ \begin{array}{lcl} {{x=2+6n,~n\in\mathbb {Z},} \\ {x=3+6k,~k\in\mathbb {Z},}} \end{array} \right.$