Question

Срочно!!!!!!!! решите все задания во вложении!!!

Answer 1

1)sinx=a, -1≤a≤1  ⇒  x=(-1)^n *arcsina+πn, n∈Z

2)cosx=√3/2,  x=±arccos√3/2+2πn, x=±π/6+2πn, n∈Z

3)sin2x=√2/2,  2x=(-1)^n *arcsin√2/2+πn, 2x=(-1)^n*π/4+πn,  x=(-1)^n*π/8+πn/2, n∈Z

4)3-√3tg(x-π/10)=0, tg(x-π/10)=3/√3=√3, x-π/10=arctg√3+πn, x-π/10=π/3+πn,

                                                   x=π/10+π/3+πn, x=13π/30+πn, n∈Z 

5) sinx≤1/2, 5π/6+2πn≤x≤13π/6+2πn, n∈Z

6)cosx>√2/2,  -π/4+2πn<x<π/4+2πn, n∈Z

7)sinx>-√2/2, -π/4+2πn<x<5π/4+2πn, n∈Z 

8)cos(2x+π/6)≤-1/2,  2π/3+2πn≤2x+π/6≤4π/3+2πn,

                                          π/2+2πn ≤2x≤7π/6+2πn 

                                           π/4+πn≤x≤7π/12+πn, n∈Z  

9) cosx=a, x=±arccosx+2πn? n∈Z, -1≤a≤1

10) sinx=1/2, x=(-1)^n*π/6+πn, n∈Z

11) cosx/3=1/2, x/3=±π/3+2πn, x=±π+6πn, n∈Z

12)3tg(2x+π/10)-3√3=0,   tg(2x+√/10)=√3,  2x+π/10=π/3+πn, 2x=7π/30+πn,

x=7π/60+πn/2, n∈Z

13)tgx≥1, π/4+πn ≤x<π/2+πn, n∈Z

14) sinx<√2/2,  3π/4+2πn<x<9π/4+2πn, n∈z

15)cosx≤-1/2,  π/3+2πn≤x≤5π/3+2πn, n∈Z

16)3tg(x/4-π/3)≥√3, tg(x/4-π/3)≥√3/3, π/6+πn≤x/4-π/3<π/2+πn,

                              3π/6+πn≤x/4<5π/6+πn,  2π+4πn≤x<10π/2+4πn, n∈Z