Question

Sin(x/4-pi/3)=- корень из 3/2

Answer 1

$sin( \dfrac{x}{4}- \dfrac{ \pi }{3})=- \dfrac{ \sqrt{3} }{2} \\ \left[\begin{array}{I} \dfrac{x}{4}- \dfrac{\pi}{3}= -\dfrac{ \pi }{3}+2 \pi k \\ \\ \dfrac{x}{4}- \dfrac{\pi}{3}= \pi + \dfrac{ \pi }{3}+2 \pi k \end{array}} \Leftrightarrow \left[\begin{array}{I} x=8 \pi k \\ x= \dfrac{20 \pi }{3}+8 \pi k \end{array}}$

Ответ: $\left[\begin{array}{I} x=8 \pi k \\ x= \dfrac{20 \pi }{3}+8 \pi k \end{array}} ;\ k \in Z$