Подробно решение распишите пожалуйста [tex]4sin^{2} 3x\ \textless \ 3[/tex]. Created by donkeyboy0192. algebra-ru

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Подробно решение распишите пожалуйста
[tex]4sin^{2} 3x\ \textless \ 3[/tex]

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NNNLLL54

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$4sin^23x\ \textless \ 3\; \; \Rightarrow \; \; 4sin^23x-3\ \textless \ 0\\\\(2sin3x-\sqrt3)(2sin3x+\sqrt3)\ \textless \ 0\\\\t=sin3x\; ,\; \; \; (2t-\sqrt3)(2t+\sqrt3)\ \textless \ 0\\\\Znaki:\; \; \; +++(-\frac{\sqrt3}{2})---(\frac{\sqrt3}{2})+++\; \; \; \; \; \; -\frac{\sqrt3}{2}\ \textless \ t\ \textless \ \frac{\sqrt3}{2}\\\\\left \{ {{sin3x\ \textless \ \frac{\sqrt3}{2}} \atop {sin3x\ \textgreater \ -\frac{\sqrt3}{2}}} \right. \; \left \{ {{-\frac{4\pi}{3}+2\pi n\ \textless \ 3x\ \textless \ \frac{\pi}{3}+2\pi n\; ,\; n\in Z} \atop {-\frac{4\pi }{3}+2\pi k\ \textless \ 3x\ \textless \ -\frac{\pi}{3}+2\pi k\; ,\; k\in Z}} \right. \; \; \Rightarrow$

$\left [ {{\frac{2\pi}{3}+2\pi m\ \textless \ 3x\ \textless \ \frac{4\pi}{3}+2\pi m\; ,\; m\in Z} \atop {-\frac{\pi}{3}+2\pi l\ \textless \ 3x\ \textless \ \frac{\pi}{3}+2\pi l\; ,\; l\in Z}} \right. \; \left [ {{\frac{2\pi}{9}+\frac{2\pi m}{3}\ \textless \ x\ \textless \ \frac{4\pi }{9}+\frac{2\pi m}{3}\; ,\; m\in Z} \atop {-\frac{\pi}{9}+\frac{2\pi l}{3}\ \textless \ x\ \textless \ \frac{\pi}{9}+\frac{2\pi l}{3}}\; ,l\in Z} \right.$

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donkeyboy0192 October 2021 | 0 Ответы

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