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zatuliy
@zatuliy
July 2022
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Решите тригонометрическое уровнение
2*sin(x+π/3)= - 1
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nKrynka
Решение
2*sin(x+π/3)= - 1
sin(x+π/3)= - 1/2
x +
π/3 = (-1)^n arcsin(- 1/2) + πk, k ∈ Z
x +
π/3 = (-1)^(n+1) arcsin(1/2) + πk, k ∈ Z
x +
π/3 = (-1)^(n+1) * (
π/6)
+ πk, k ∈ Z
x
= (-1)^(n+1) * (
π/6)
-
π/3
+ πk, k ∈ Z
1 votes
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Answers & Comments
2*sin(x+π/3)= - 1
sin(x+π/3)= - 1/2
x + π/3 = (-1)^n arcsin(- 1/2) + πk, k ∈ Z
x + π/3 = (-1)^(n+1) arcsin(1/2) + πk, k ∈ Z
x + π/3 = (-1)^(n+1) * (π/6) + πk, k ∈ Z
x = (-1)^(n+1) * (π/6) - π/3 + πk, k ∈ Z