Номер 244(полностью) и номер 246(2,4). Created by stiklin. algebra-ru

Номер 244(полностью) и номер 246(2,4)...

stiklin @stiklin

August 2022 1 39 Report

Номер 244(полностью) и номер 246(2,4)

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oganesbagoyan

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Task/26536132
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244 .
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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 * * *
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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 .
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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 .
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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 .
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246.
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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 .
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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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