Question

CРОЧНО! 35 БАЛЛОВ!

Решить неравенство.

1)Sin х≤1/2

2)2cos 2x ≥ 1

Answer 1

Ответ:

$1)\ \ sinx\leq \dfrac{1}{2}\\\\-\dfrac{7\pi }{6}+2\pi n\leq x\leq \dfrac{\pi}{6}+2\pi n\ ,\ n\in Z\\\\\\x\in \Big(-\dfrac{7\pi }{6}+2\pi n\ ;\ \dfrac{\pi}{6}+2\pi n\ \Big)\ ,\ n\in Z$

$2)\ \ \ 2\cdot cos2x\geq 1\ \ \ \Rightarrow \ \ \ cos2x\geq \dfrac{1}{2}\ \ ,\\\\\\-\dfrac{\pi}{3}+2\pi n\leq 2x\leq \dfrac{\pi}{3}+2\pi n\ ,\ n\in Z\\\\\\\-\dfrac{\pi}{6}+\pi n\leq x\leq \dfrac{\pi}{6}+\pi n\ ,\ n\in Z\\\\\\x\in \Big(-\dfrac{\pi}{6}+\pi n\ ;\ \dfrac{\pi}{6}+\pi n\ \Big)\ ,\ n\in Z$