Question

треб розвязати тригонометричне рівняння:
2sin(x/6+П/12)+2=0

Answer 1

$2Sin(\frac{x}{6}+\frac{\pi }{12})+2=0\\\\2Sin(\frac{x}{6}+\frac{\pi }{12})=-2\\\\Sin(\frac{x}{6}+\frac{\pi }{12})=-1\\\\\frac{x}{6}+\frac{\pi }{12}=-\frac{\pi }{2}+2\pi n,n\in Z\\\\\frac{x}{6}=-\frac{\pi }{12} -\frac{\pi }{2} +2\pi n,n\in Z\\\\\frac{x}{6}=-\frac{7\pi }{12}+2\pi n,n\in Z\\\\x=-\frac{7\pi }{2}+12\pi n,n\in Z$