Question

СРОЧНО. ПОМОГИТЕ ПЖ.
50 БАЛЛОВ! За решение 2 примеров

Answer 1

$sin(2x)=-\frac{1}{2}\\\\ 2x=-\frac{\pi}{6}+2\pi n,\ n\in Z\ \ \ or\ \ \ 2x=-\frac{5\pi}{6}+2\pi n,\ n\in Z\\\\ x=-\frac{\pi}{12}+\pi n,\ n\in Z\ \ \ or\ \ \ x=-\frac{5\pi}{12}+\pi n,\ n\in Z$

входящие в интервал $[-\frac{\pi}{2};\ \pi]$ решения:
$-\frac{\pi}{12},\ -\frac{\pi}{12}+\pi,\ -\frac{5\pi}{12},\ -\frac{5\pi}{12}+\pi\\\\ -\frac{\pi}{12},\ \frac{11\pi}{12},\ -\frac{5\pi}{12},\ \frac{7\pi}{12}$

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$cos(4x)=\frac{\sqrt{2}}{2}\\\\ 4x=\pm\frac{\pi}{4}+2\pi n,\ n\in Z\\\\ x=\pm\frac{\pi}{16}+\frac{\pi n}{2},\ n\in Z$

входящие в интервал $[0;\ \pi]$ решения:
$\frac{\pi}{16},\ \frac{\pi}{16}+\frac{\pi}{2},\ -\frac{\pi}{16}+\frac{\pi}{2},\ -\frac{\pi}{16}+\pi\\\\ \frac{\pi}{16},\ \frac{9\pi}{16},\ \frac{7\pi}{16},\ \frac{15\pi}{16}$