Question

Помогите решить: 1) cos(x+п/4)=1 2) sin (3п/2-x)=-1 3) sin(-x)=-0,5 4) tgx/2=корень из 3 5)cos(2x-п/3)=корень из3/2

Answer 1

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1) x+π/4 =2π*k , k∈ Z .
x= - π/4 x+2π*k , k∈ Z .
2) sin(3π/2 -x) = -1;
- cosx = -1;
cosx  =1;
x=2π*k  , k ∈ Z .
3) sin(-x) = -1/2 ;
- sinx = -1/2
sinx= 1/2;
x= (-1)^(k)*π/6+π*k , k ∈Z.
4) tq(x/2) =√3 ;        [   (tqx)/2 =√3 ];
x/2  = π/3 +π*k , k ∈ Z .
x=2π/3 +2π*k , k ∈ Z.
5) cos(2x-π/3) =(√3)/2;
 [2x - π/3 =  - π/6 +2π*k ,k ∈ Z  ; 2x - π/3 =   π/6 +2π*k ,k ∈ Z. 
 [2x = π/3  - π/6 +2π*k ,k ∈ Z  ; 2x = π/3 +  π/6 +2π*k ,k ∈ Z 
 [2x = π/6 +2π*k ,k ∈ Z  ; 2x = π/2 +2π*k ,k ∈ Z .

x = π/12 +π*k ,k ∈ Z  ; 
x = π/4 +π*k ,k ∈ Z .