![-1 \leq Sinx \leq 1 \\ -2 \leq -2 Sinx \leq 2 \\ -2 +5\leq 5-2sinx \leq 2+5 \\ \\ 3 \leq 5-2sinx \leq 7 \\ \\ y=[3;7]](https://tex.z-dn.net/?f=-1+%5Cleq+Sinx+%5Cleq+1+%5C%5C+-2+++%5Cleq++-2+Sinx+++%5Cleq++2+%5C%5C+-2+%2B5%5Cleq+5-2sinx+%5Cleq+2%2B5+%5C%5C+%5C%5C+3+%5Cleq+5-2sinx+%5Cleq+7+%5C%5C+%5C%5C+y%3D%5B3%3B7%5D)
<u>Ответ: область значений функции промежуток [3;7].</u>
1) Из формулы n-го члена арифметической прогрессии имеем, что
![a_8=a_1+7d=a_1+2d+5d=a_3+5d=10+5\cdot3=25](https://tex.z-dn.net/?f=a_8%3Da_1%2B7d%3Da_1%2B2d%2B5d%3Da_3%2B5d%3D10%2B5%5Ccdot3%3D25)
2) Аналогично
![a_6=a_1+5d=a_1+2d+3d=a_3+3d=6+3\cdot1=9](https://tex.z-dn.net/?f=a_6%3Da_1%2B5d%3Da_1%2B2d%2B3d%3Da_3%2B3d%3D6%2B3%5Ccdot1%3D9)
3) По формуле n-го члена арифметической прогрессии найдем a11
![a_{11}=a_1+10d=12+10\cdot(-4)=12-40=-28](https://tex.z-dn.net/?f=a_%7B11%7D%3Da_1%2B10d%3D12%2B10%5Ccdot%28-4%29%3D12-40%3D-28)
4) Первый член арифметической прогрессии по формуле n-го члена этой же прогрессии:
![a_9=a_1+8d;~~\Rightarrow~~~a_1=a_9-8d=11-8\cdot2=-5](https://tex.z-dn.net/?f=a_9%3Da_1%2B8d%3B~~%5CRightarrow~~~a_1%3Da_9-8d%3D11-8%5Ccdot2%3D-5)
Сумма первых 12 членов арифметической прогрессии:
![S_{12}= \dfrac{2a_1+11d}{2}\cdot12=6(2a_1+11d)=6\cdot(2\cdot3+11\cdot2)= 168](https://tex.z-dn.net/?f=S_%7B12%7D%3D+%5Cdfrac%7B2a_1%2B11d%7D%7B2%7D%5Ccdot12%3D6%282a_1%2B11d%29%3D6%5Ccdot%282%5Ccdot3%2B11%5Ccdot2%29%3D+168)
5)
![a_1-a_2+a_3-a_4+...+a_{25}-a_{26}+a_{27}=](https://tex.z-dn.net/?f=a_1-a_2%2Ba_3-a_4%2B...%2Ba_%7B25%7D-a_%7B26%7D%2Ba_%7B27%7D%3D)
![=a_1+a_3+a_5+...+a_{25}+a_{27}-(a_2+a_4+...+a_{26})=\\ \\ =13a_1+2d+4d+...26d-(14a_1+d+3d+...+25d)=\\ \\ =-a_1+13d=-3+13\cdot2=23](https://tex.z-dn.net/?f=%3Da_1%2Ba_3%2Ba_5%2B...%2Ba_%7B25%7D%2Ba_%7B27%7D-%28a_2%2Ba_4%2B...%2Ba_%7B26%7D%29%3D%5C%5C+%5C%5C+%3D13a_1%2B2d%2B4d%2B...26d-%2814a_1%2Bd%2B3d%2B...%2B25d%29%3D%5C%5C+%5C%5C+%3D-a_1%2B13d%3D-3%2B13%5Ccdot2%3D23)
1) (sin a cos a - sin a/ cos a)/ cos a - 1= tg a
2) sin2a
√(x^2-4x+13)² =( 0,5x+2)²
x² -4x+13 =0,25x²<span>+2х+4
</span>0.75х² -6х+9=0 для упрощения почленно домножим на 4/3
х²-8х+12=0
D=64-48=16 √D=4
x₁=(8+4)/2=6
x₂=(8-4)/2=2