Question

Решите,пжл : sin(φ-π/3)=1/2

Answer 1

$Sin( alpha - frac{ pi }{3})= frac{1}{2} \\ alpha - frac{ pi }{3}=arcSin frac{1}{2} +2 pi n\\ alpha - frac{ pi }{3}= frac{ pi }{6} +2 pi n\\ alpha _{1}= frac{ pi }{3} + frac{ pi }{6}+ 2pi n\\ alpha _{1} = frac{ pi }{2}+2 pi n \\\ alpha - frac{ pi }{3}= pi -arcSin frac{1}{2}+2 pi n\\ alpha - frac{ pi }{3}= pi - frac{ pi }{6} +2 pi n \\ alpha - frac{ pi }{3}= frac{5 pi }{6} +2 pi n\\ alpha _{2}= frac{ pi }{3}+ frac{5 pi }{6}+ 2 pi n\\ alpha _{2}= frac{7 pi }{6} +2 pi n$n∈z