Question

Даю 40 баллов, помогите решить неравенство тригонометрия ​

Answer 1

$Sin(x+\frac{\pi }{4})\leq\frac{1}{2}\\\\-\pi- arc Sin\frac{1}{2}+2\pi n \leq x+\frac{\pi }{4}\leq arc Sin\frac{1}{2}+2\pi n,n\in Z\\\\-\pi-\frac{\pi }{6}+2\pi n\leq x+\frac{\pi }{4}\leq \frac{\pi }{6}+2\pi n,n\in Z\\\\-\frac{7\pi }{6}+2\pi n\leq x+\frac{\pi }{4} \leq \frac{\pi }{6}+2\pi n,n\in Z\\\\-\frac{7\pi }{6}-\frac{\pi }{4}+2\pi n\leq x \leq\frac{\pi }{6}-\frac{\pi }{4}+2\pi n,n\in Z$

$-\frac{17\pi }{12}+2\pi n\leq x\leq -\frac{\pi }{12}+2\pi n,n\in Z\\\\Otvet:\boxed {x\in[-\frac{17\pi }{12}+2\pi n;-\frac{\pi }{12}+2\pi n],n\in Z}$