![6sin (\frac{23\pi}{4} )\cdot sin \frac{x}{2} +cosx=3\\\\\star \; \; sin \frac{23\pi}{4} =sin(6\pi -\frac{\pi}{4})=sin(-\frac{\pi}{4})=-sin\frac{\pi}{4}=-\frac{\sqrt2}{2}\; \; \; \star \\\\-3\sqrt2\cdot sin\frac{x}{2}+(1-2sin^2\frac{x}{2})-3=0\; ,\quad \star \; cos \alpha =1-2sin^2\frac{ \alpha }{2}\; \star \\\\2sin^2 \frac{x}{2}+3\sqrt2\cdot sin \frac{x}{2} }+2=0\\\\D=18-16=2\\\\(sin\frac{x}{2})_1= \frac{-3\sqrt2-\sqrt2}{4}=-\sqrt2\ \textless \ -1\; ,\; net\; reshenij](https://tex.z-dn.net/?f=6sin+%28%5Cfrac%7B23%5Cpi%7D%7B4%7D+%29%5Ccdot+sin+%5Cfrac%7Bx%7D%7B2%7D+%2Bcosx%3D3%5C%5C%5C%5C%5Cstar+%5C%3B+%5C%3B+sin+%5Cfrac%7B23%5Cpi%7D%7B4%7D+%3Dsin%286%5Cpi+-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3Dsin%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-sin%5Cfrac%7B%5Cpi%7D%7B4%7D%3D-%5Cfrac%7B%5Csqrt2%7D%7B2%7D%5C%3B+%5C%3B+%5C%3B+%5Cstar+%5C%5C%5C%5C-3%5Csqrt2%5Ccdot+sin%5Cfrac%7Bx%7D%7B2%7D%2B%281-2sin%5E2%5Cfrac%7Bx%7D%7B2%7D%29-3%3D0%5C%3B+%2C%5Cquad+%5Cstar+%5C%3B+cos+%5Calpha+%3D1-2sin%5E2%5Cfrac%7B+%5Calpha+%7D%7B2%7D%5C%3B+%5Cstar+%5C%5C%5C%5C2sin%5E2+%5Cfrac%7Bx%7D%7B2%7D%2B3%5Csqrt2%5Ccdot+sin+%5Cfrac%7Bx%7D%7B2%7D+%7D%2B2%3D0%5C%5C%5C%5CD%3D18-16%3D2%5C%5C%5C%5C%28sin%5Cfrac%7Bx%7D%7B2%7D%29_1%3D+%5Cfrac%7B-3%5Csqrt2-%5Csqrt2%7D%7B4%7D%3D-%5Csqrt2%5C+%5Ctextless+%5C+-1%5C%3B+%2C%5C%3B+net%5C%3B+reshenij)
![(sin\frac{x}{2})_2= \frac{-3\sqrt2+\sqrt2}{4} =-\frac{\sqrt2}{2}](https://tex.z-dn.net/?f=%28sin%5Cfrac%7Bx%7D%7B2%7D%29_2%3D++%5Cfrac%7B-3%5Csqrt2%2B%5Csqrt2%7D%7B4%7D+%3D-%5Cfrac%7B%5Csqrt2%7D%7B2%7D)
![\frac{x}{2}=(-1)^{n}(-\frac{\pi}{4})+\pi n=(-1)^{n+1}\frac{\pi}{4}+\pi n,\; n\in Z\\\\x=(-1)^{n+1}\frac{\pi}{2}+2\pi n,\; n\in Z](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%3D%28-1%29%5E%7Bn%7D%28-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%2B%5Cpi+n%3D%28-1%29%5E%7Bn%2B1%7D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi+n%2C%5C%3B+n%5Cin+Z%5C%5C%5C%5Cx%3D%28-1%29%5E%7Bn%2B1%7D%5Cfrac%7B%5Cpi%7D%7B2%7D%2B2%5Cpi+n%2C%5C%3B+n%5Cin+Z)
хЄ[-5;7,85] ⇒ x=-3П/2 ; -П/2 ; П/2 ; 3П/2 .
-5 радиан~ -286,5°
7,85 радиан ~ 449,8°
40/8=5 в 5 раз дима дольше гулял. 40/8=5 минут дима лепил
(0,8 * 1,25 - 1,25) : 1/8 = - 2
1) 0,8 * 1,25 = 1
2) 1 - 1,25 = - 0,25
3) - 0,25 : 1/8 = - 0,25 : 0,125 = - 2
20 единиц > 8 единиц
должно быть так
14 ч 56 мин - 9 ч 2 мин = 5 ч 54 мин продолжительность короткого дня
21 ч 27 мин - 2 ч 37 мин = 18 ч 50 мин продолжительность длинного дня
18 ч 50 мин - 5ч 54 мин = 12 ч 56 мин один короче другого