Question

2sin(3x-пи делённое на 4)=-корень из 2

Answer 1

$2 sin(3x - frac{pi}{4} ) = - sqrt{2} \ sin(3x - frac{pi}{4} ) = - frac{ sqrt{2} }{2} \ 3x - frac{pi}{4} = ( - 1)^{n} arcsin( - frac{ sqrt{2} }{2} ) + pi n \ 3x - frac{pi}{4} = ( - 1)^{n + 1} frac{pi}{4} + pi n \ 3x = ( - 1)^{n + 1} frac{pi}{4} - frac{pi}{4} + pi n \ x = ( - 1)^{n + 1} frac{pi}{12} - frac{pi}{12} + frac{pi}{3} n \ x = ( {( - 1)}^{n + 1} - 1) frac{pi}{12} + frac{pi}{3} n, : n in Z$