1) sin x < √2/2
-π-arcsin(√2/2)+2πn<х<arcsin(√2/2)+2πn;n∈Z;
-π-π/4+2πn<х<π/4+2πn;n∈Z;
-5π/4+2πn<х<π/4+2πn;n∈Z;
2) cos x ≤ 1/2
arccos(1/2)+2πn≤х≤2π-arccos(1/2)+2πn;n∈Z;
π/3+2πn≤х≤2π-π/3+2πn;n∈Z;
π/3+2πn≤х≤5π/3+2πn;n∈Z;
3) tg x ≥ 1
arctg1+πn≤x<π/2+πn;n∈Z;
π/4+πn≤x<π/2+πn;n∈Z;
4) ctg x > √3
πn<x<arcctg√3+πn;n∈Z;
πn<x<π/6+πn;n∈Z;
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Answers & Comments
1) sin x < √2/2
-π-arcsin(√2/2)+2πn<х<arcsin(√2/2)+2πn;n∈Z;
-π-π/4+2πn<х<π/4+2πn;n∈Z;
-5π/4+2πn<х<π/4+2πn;n∈Z;
2) cos x ≤ 1/2
arccos(1/2)+2πn≤х≤2π-arccos(1/2)+2πn;n∈Z;
π/3+2πn≤х≤2π-π/3+2πn;n∈Z;
π/3+2πn≤х≤5π/3+2πn;n∈Z;
3) tg x ≥ 1
arctg1+πn≤x<π/2+πn;n∈Z;
π/4+πn≤x<π/2+πn;n∈Z;
4) ctg x > √3
πn<x<arcctg√3+πn;n∈Z;
πn<x<π/6+πn;n∈Z;