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stiklin
@stiklin
August 2022
1
41
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Номер 244(полностью) и номер 246(2,4)
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oganesbagoyan
Verified answer
Task/26536132
--------------------
244 .
-------
1)
sin(x -π/3) =1/2 ;
x - π/3 =(-1)^n (π/6) + πn , n∈ Z. * * * n - целое число * * *
x = π/3 + (-1)^n (
π/6) +πn , n∈ Z.
или разделяя для четных и нечетных n
x₁ = π/2 + 2
πk , k∈ Z ; * * *
n =2k
→ четное число * * *
x₂ = 7π/6 +2
πk , k∈ Z .
* * *
n =2k+1
→четное число * * *
-------
2)
cos(x+π/4) = -(√3) /2 ;
x+π/4 = ±(π -π/6) +2πn, n∈ Z .
x = - π/4 ± 5π
/
6 +2πn, n∈ Z .
или разделяя
x₁ = 7
π
/12 + 2
πn , n ∈ Z ;
x₂ = - π/12 +
(2k -1)
π
, k∈ Z .
-------
3)
tg(2x -π/6) =1 ;
2x -π/6 =π/4 +πn , n ∈ Z ;
2x=π/6 +π/4 +πn , n ∈ Z ;
2x=5π/12 +πn , n
∈ Z ;
x= 5π/24 + (π/2)*n ,n ∈Z .
-------
4)
ctg(x/2 +π/8) =√3 ;
x/2 +π/8 =π/6 + πn , n ∈
Z ;
x/2 = π/6 - π/8 + πn , n ∈ Z ;
x/2 = π/24 + πn , n ∈
Z ;
x = π/12 + 2πn , n ∈
Z .
-------------------------------------
246.
-------
2)
2cos(2x +π/3) =√3 ;
cos(2x +
π/3) =(√3) /2 ;
2x +π/3 = ±π/3 +2πn , n∈ Z ;
2x = - π/3 ±π/3 +2πn , n∈
Z ;
x = - π/6 ±π/6 + πn , n∈ Z ;
или разделяя
x₁ = -
π
/3 +
πn , n ∈ Z ;
x₂ =
π
n
, n ∈ Z .
-------
4)
ctg(2x + π/3) =√3 ;
2x + π/3 =π/6 + πn , n ∈ Z ;
2x = - π/3+ π/6 + πn ,
n ∈ Z ;
2x = -
π/6+
πn ,
n ∈ Z ;
x = - π/12+ (π/2)*n ,
n ∈ Z.
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Answers & Comments
Verified answer
Task/26536132--------------------
244 .
-------
1)
sin(x -π/3) =1/2 ;
x - π/3 =(-1)^n (π/6) + πn , n∈ Z. * * * n - целое число * * *
x = π/3 + (-1)^n (π/6) +πn , n∈ Z.
или разделяя для четных и нечетных n
x₁ = π/2 + 2πk , k∈ Z ; * * * n =2k → четное число * * *
x₂ = 7π/6 +2πk , k∈ Z . * * * n =2k+1 →четное число * * *
-------
2)
cos(x+π/4) = -(√3) /2 ;
x+π/4 = ±(π -π/6) +2πn, n∈ Z .
x = - π/4 ± 5π / 6 +2πn, n∈ Z .
или разделяя
x₁ = 7π/12 + 2πn , n ∈ Z ;
x₂ = - π/12 + (2k -1)π , k∈ Z .
-------
3)
tg(2x -π/6) =1 ;
2x -π/6 =π/4 +πn , n ∈ Z ;
2x=π/6 +π/4 +πn , n ∈ Z ;
2x=5π/12 +πn , n ∈ Z ;
x= 5π/24 + (π/2)*n ,n ∈Z .
-------
4)
ctg(x/2 +π/8) =√3 ;
x/2 +π/8 =π/6 + πn , n ∈ Z ;
x/2 = π/6 - π/8 + πn , n ∈ Z ;
x/2 = π/24 + πn , n ∈ Z ;
x = π/12 + 2πn , n ∈ Z .
-------------------------------------
246.
-------
2)
2cos(2x +π/3) =√3 ;
cos(2x +π/3) =(√3) /2 ;
2x +π/3 = ±π/3 +2πn , n∈ Z ;
2x = - π/3 ±π/3 +2πn , n∈ Z ;
x = - π/6 ±π/6 + πn , n∈ Z ;
или разделяя
x₁ = - π/3 + πn , n ∈ Z ;
x₂ = π n , n ∈ Z .
-------
4)
ctg(2x + π/3) =√3 ;
2x + π/3 =π/6 + πn , n ∈ Z ;
2x = - π/3+ π/6 + πn , n ∈ Z ;
2x = - π/6+ πn , n ∈ Z ;
x = - π/12+ (π/2)*n , n ∈ Z.