Question

Решите тригонометрическое уравнение: 2sin(3x-п/5)+1=0

Answer 1

sin(3x-pi/5)=-1/2
3x-pi/5=(-1)^(n+1)*arcsin(1/2) + pi*k, k=+-1,2...
3x-pi/5=(-1)^(n+1)*pi/6 + pi*k, k=+-1,2...
3x=(-1)^(n+1)*pi/6 + pi/5 + pi*k, k=+-1,2...
x=(-1)^(n+1)*pi/18 + pi/15 + pi*k/3, k=+-1,2...

Answer 2

sin(3x-π/5)=-1/2
3x-π/5=-π/6+2πn⇒3x=π/5-π/6+2πn=π/30+2πn⇒x=π/90+2πn/3
3x-π/5=7π/6+2πn⇒3x=π/5+7π/6+2πn=41π/30+2πn⇒x=41π/90+2πn/3