1) sin x≥ -√2
2
-3π + 2πn ≤ x ≤ -π +2πn, n∈Z
4 4
Ответ: (-3π + 2πn; -π + 2πn), n∈Z
4 4
2) cos x/4 < 0
пусть x/4 = t
cost <0 <br>π/2 + 2πn < t < 3π + 2πn, n∈Z
2
π + 2πn < x/4 < 3π + 2πn, n∈Z
2 2
4 * π + 4 * 2πn < x < 4 *3π + 4*2πn, n∈Z
2 2
2π+8πn < x < 6π +8πn, n∈Z
Ответ: (2π+8πn; 6π+8πn) , n∈Z
3) √3 tgx <3<br> tgx < 3/√3
tgx < 3√3
√3*√3
tgx <√3<br>-π/2 + πn Ответ:(-π/2 +πn; π/3 +πn), n∈Z
4) 2 cos(2x +π/4) >√2
cos(2x+π/4) > √2
2
Пусть 2х+π/4=t
cost > √2
2
-π/4 + 2πn -π/4 + 2πn < 2x+π/4 < π/4 + 2πn, n∈Z<br>-π/4 - π/4 +2πn < 2x < π/4 - π/4 + 2πn, n∈Z<br> -π/2 + 2πn < 2x < 2πn, n∈Z
-π/4 + πn < x < πn, n∈Z<br>Ответ: (-π/4 + πn; πn), n∈Z