Question

Помогите с решением:

Answer 1

$Sin\frac{\pi(x-9) }{12}=\frac{\sqrt{3}}{2}\\\\1)\frac{\pi(x-9) }{12}=arcSin\frac{\sqrt{3} }{2}+2\pi n,n\in Z\\\\\frac{\pi(x-9)}{12}=\frac{\pi}{3} +2\pi n,n\in Z\\\\\frac{x-9}{12}=\frac{1}{3}+2n,n\in Z\\\\x-9=4+24n,n\in Z\\\\x=13+24n,n\in Z\\\\n=0\Rightarrow x_{1}=13\\\\2)\frac{\pi(x-9)}{12}=\pi-arcSin\frac{\sqrt{3} }{2}+2\pi n,n\in Z\\\\\frac{\pi(x-9)}{12}=\frac{2\pi }{3}+2\pi n,n\in Z\\\\\frac{x-9}{12}=\frac{2}{3} +2n,n\in Z\\\\x-9=8+24n, n\in Z\\\\x=17+24n,n\in Z$

$n=0\Rightarrow x_{1} =17\\\\Otvet:13$