Question

sin(2(x - 1)) = -1/2

Answer 1

Ответ:

$\boldsymbol{x _1 = \frac{7 \pi}{12} + 1 + \pi n,n \in Z} \\ \boldsymbol{x_2 = \frac{11 \pi}{12} + 1 + \pi k,k \in Z}$

Объяснение:

$\displaystyle sin\Big(2 (x - 1)\Big) = - \frac{1}{2} \\ 2(x - 1) = \frac{7 \pi}{6} + 2 \pi n ,n \in Z \\ 2(x - 1) = \frac{11 \pi}{6} + 2 \pi k,k \in Z \\ 2x - 2 = \frac{7 \pi}{6} + 2 \pi n,n \in Z \\ 2x - 2 = \frac{11 \pi}{6} + 2 \pi k,k \in Z \\ 2x = \frac{7 \pi}{6} + 2 + 2 \pi n,n \in Z|:2 \\ 2x = \frac{11\pi}{6} + 2 \pi k,k \in Z|:2 \\ \boldsymbol{x _1 = \frac{7 \pi}{12} + 1 + \pi n,n \in Z} \\ \boldsymbol{x_2 = \frac{11 \pi}{12} + 1 + \pi k,k \in Z}$