Question

2sin(3x + p/3)+корень из 3=0

Answer 1

Объяснение:

$2\sin(3x+\frac{\pi}{3})+\sqrt{3}=0\\ \\ \sin(3x+\frac{\pi}{3})=-\frac{\sqrt{3}}{2}\\ \\ 3x+\frac{\pi}{3}=(-1)^{k+1}\cdot\frac{\pi}{3}+\pi k,k \in Z\\ \\ 3x=(-1)^{k+1}\cdot\frac{\pi}{3}-\frac{\pi}{3}+\pi k,k \in Z\\ \\ x=(-1)^{k+1}\cdot\frac{\pi}{9}-\frac{\pi}{9}+\frac{\pi k}{3},k \in Z$

Answer 2

$2\sin \Big(3x+\dfrac{\pi}3\Big)+\sqrt3=0\\\\\sin \Big(3x+\dfrac{\pi}3\Big)=-\dfrac{\sqrt3}2\\\\1)~3x+\dfrac{\pi}3=-\dfrac{\pi}3+2\pi n;~~~3x=-\dfrac{2\pi}3+2\pi n\\\\~~~\boxed{\boldsymbol{x_1=-\dfrac{2\pi}9+\dfrac{2\pi n}3;~~~n\in Z}}\\\\\\2)~3x+\dfrac{\pi}3=-\dfrac{2\pi}3+2\pi k;~~~3x=-\pi+2\pi k\\\\~~~\boxed{\boldsymbol{x_2=\dfrac{-\pi+2\pi k}3;~~~k\in Z}}$