Задача 25282 ...
Условие
2)√3 sinx+cosx=0;[π;3π]
математика 10-11 класс
922
Решение
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sin((π/3)–x)=-sin(x-(π/3))
sin(x-(π/3))=-1/2
x-(π/3)=(π/6)+2πk или x-(π/3)=(5π/6)+2πn, k, n ∈ Z
x=(π/3)+(π/6)+2πk или x=(π/3)+(5π/6)+2πn, k, n ∈ Z
x=(π/2)+2πk или x=(7π/6)+2πn, k, n ∈ Z
О т в е т. (π/2)+2πk ; (7π/6)+2πn, k, n ∈ Z
2) tgx=-1/sqrt(3)
x=-(π/6)+πk, k ∈ Z
x1=-(π/6)+π*2=11π/6∈ [π;3π]
x2=-(π/6)+π*3=17π/6 ∈ [π;3π]