Предмет: Алгебра, автор: gfdkj135

Розв’яжіть рівняння sin3х =1/2

Ответы

Автор ответа: Анетка125

sin3x=0.5
3x=arcsin 0.5 +2pin n∈Z
3x=pi-arcsin 0.5 +2pin n∈Z
3x=arcsin pi/6 +2pin n∈Z
3x=pi-arcsin pi/6+2pin n∈Z
x=arcsin pi/18 +2pin/3 n∈Z
x=pi-arcsin pi/18 +2pin/3 n∈Z

Автор ответа: GreatFilter

$sinx=a\\ sinx=(-1)^karcsin a+ \pi k$ k∈Z

$sin3x=н\\ 3x=(-1)^karcsin н+ \pi k$ k∈Z
$3x=(-1)^k \frac{ \pi }{6} + \pi k$ k∈Z
$x=(-1)^k \frac{ \pi }{18} + \frac{\pi k}{3}$ k∈Z

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