Question

Розвяжіть тригонометричні рівняння​

Answer 1

3)

$\displaystyle sin(4x-\frac{\pi }{3} ) =-1 , 4x-\frac{\pi }{3} = -\frac{\pi }{2} +2\pi n,\\4x=\frac{\pi }{3} -\frac{\pi }{2} +2\pi n , 4x=-\frac{\pi }{6} +2 \pi n\\x=\frac{-\pi }{24} +\frac{\pi n}{2}$, n∈Z

4)

$\displaystyle 2sin(2x+\frac{\pi }{6} ) = \sqrt{3} , \\\displaystyle sin(2x+\frac{\pi }{6} ) = \frac{\sqrt{3} }{2} ,\\2x+\frac{\pi }{6} = \frac{\pi }{3} +2\pi n, 2x=\frac{\pi }{3} -\frac{\pi }{6} +2\pi n , 2x=\frac{\pi }{6} +2 \pi n , x=\frac{\pi }{12} +\pi n\\2x+\frac{\pi }{6} = \frac{2\pi }{3} +2\pi n, 2x=\frac{2\pi }{3} -\frac{\pi }{6} +2\pi n , 2x=\frac{\pi }{2} +2 \pi n , x=\frac{\pi }{4} +\pi n$  ,n∈Z