Question

Алгебра. Решите неравенство

Answer 1

1. 1)

-arccos(-√2/2)+2πn<x/5<arccos(-√2/2)+2πn; n∈Z

-(π-π/4)+2πn<x/5<3π/4)+2πn; n∈Z

-15π/4+10πn<x<15π/4)+10πn; n∈Z

2) arctg(√2/2)+πn≤5х+π/3<π/2+πn; n∈Z

arctg(√2/2)+πn-π/3≤5х<π/2-π/3+πn; n∈Z

(-π/15)+(1/5)arctg(√2/2)+πn/5≤х<π/30+πn/5; n∈Z

2. 1) 6*(1-sin²x)+13sinx-8=0

-6sin²x+13sinx-8+6=0

6sin²x-13sinx+2=0

sinx=(13±√(169-48))/12=(13±11)/12

sinx=2∈∅, т.к. IsinxI≤1

sinx=1/6

х=(-1)ⁿarcsin(1/6)+πn; n∈Z