Предмет: Алгебра, автор: kocmamon2007

Решите уровнение срочно

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Автор ответа: NNNLLL54

1

Ответ:

Решить простейшие тригонометрические уравнения .

$\bf cosx=1\ \ \ \to \ \ \ x=2\pi k\ \ ,\ \ k\in Z\\\\\\sinx=-\dfrac{\sqrt2}{2}\ \ \to \ \ \ x=(-1)^{k}\, arcsin\Big(-\dfrac{\sqrt2}{2}\Big)+\pi k=(-1)^{k}\cdot \Big(-\dfrac{\pi}{4}\Big)+\pi k=\\\\{}\qquad \qquad \qquad \qquad \ \ \ \ \ =(-1)^{k+1}\cdot \dfrac{\pi }{4}+\pi k\ \ ,\ \ k\in Z\\\\\\ctgx=-\dfrac{\sqrt3}{2}\ \ \to \ \ x=arcctg\Big(-\dfrac{\sqrt3}{2}\Big)+\pi k=-arcctg\dfrac{\sqrt3}{2}+\pi k\ \ ,\ \ k\in Z$

P.S.

$\bf ctgx=-\dfrac{\sqrt3}{3}\ \ \to \ \ x=arcctg\Big(-\dfrac{\sqrt3}{3}\Big)+\pi k=-arcctg\dfrac{\sqrt3}{3}+\pi k=\\\\{}\qquad \qquad \qquad \qquad \qquad =-\dfrac{\pi }{3}+\pi k\ ,\ k\in Z$

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