Question

Тригонометрия, вообще не шарю

Answer 1

1
sin(2/x)<-√3/2
4π/3+2πn<2/x<5π/3+2πn
2π/3+πn<1/x<5π/6+πn
6/5π+1/πn<x<5/6π+1/πn,n∈z
2
cos(x/3)>√2/2
-π/4+2πn<x/3<π/4+2πn
-3π/4+6πn,x,3π/4+6πn,n∈z
3
4sin2xcos2x≥√2
2sin4x≥√2
sin4x≥⇒2/2
π/4+2πn≤4x≤3π/4+2πn
π/16+πn/2≤x≤3π/16+πn/2,n∈z
4
sinxcosπ/6-cosxsinπ/6≤1/2
sin(x-π/6)≤1/2
5π/6+2πn≤x-π/6≤13π/6+2πn
π+2πn≤x≤7π/3+2πn,n∈z
5
5sin²t>11sint+12
sint=a
5a²-11a-12>0
D=121+240=361
a1=(11-19)/10=-0,8 U a2=(19+11)/10=3
[sint<-0,8⇒π+arcsin0,8+2πn<t<2π-arcsin0,8+2πn,n∈z
[sint>3 нет решения,т.к.|sint|≤1
6
6cos²t-sint≤4
6-6sin²t-sint≤4
sint=a
6a²+a-2≥0
D=1+48=49
a1=(-1-7)/12=-2/3 U a2=(-1+7)/12=1/2
[sint≤-2/3⇒π+arcsin2/3+2πn≤t≤2π-arcsin2/3+2πn,n∈z
[sint≥1/2⇒π/6+2πn≤x≤5π/6+2πn,n∈z