1)
![\pi=180\\1.25\pi=1.25*180=225](https://tex.z-dn.net/?f=%5Cpi%3D180%5C%5C1.25%5Cpi%3D1.25%2A180%3D225)
2)
![1=\frac{\pi}{180}\\ -150=-150*\frac{\pi}{180}=-\frac{5\pi}{6}](https://tex.z-dn.net/?f=1%3D%5Cfrac%7B%5Cpi%7D%7B180%7D%5C%5C%0A-150%3D-150%2A%5Cfrac%7B%5Cpi%7D%7B180%7D%3D-%5Cfrac%7B5%5Cpi%7D%7B6%7D)
3) a)
![sin(-252)=-sin252=-sin(360-108)=sin108=sin(90+18)=\\=cos18](https://tex.z-dn.net/?f=sin%28-252%29%3D-sin252%3D-sin%28360-108%29%3Dsin108%3Dsin%2890%2B18%29%3D%5C%5C%3Dcos18)
b)
![cos1130=cos(360*3+50)=cos50=cos(90-40)=sin40](https://tex.z-dn.net/?f=cos1130%3Dcos%28360%2A3%2B50%29%3Dcos50%3Dcos%2890-40%29%3Dsin40)
4)
![2 sin (x-1)=-\sqrt2\\ sin(x-1)=-\frac{\sqrt2}{2}\\ x_1-1=\frac{5\pi}{4}+2\pi n, n\in Z=\ \textgreater \ x_1=1+\frac{5\pi}{4}+2\pi n, n\in Z\\ x_2-1=\frac{7\pi}{4}+2\pi k, k\in Z =\ \textgreater \ x_2=1+\frac{7\pi}{4}+2\pi k, k\in Z](https://tex.z-dn.net/?f=2+sin+%28x-1%29%3D-%5Csqrt2%5C%5C%0Asin%28x-1%29%3D-%5Cfrac%7B%5Csqrt2%7D%7B2%7D%5C%5C%0Ax_1-1%3D%5Cfrac%7B5%5Cpi%7D%7B4%7D%2B2%5Cpi+n%2C+n%5Cin+Z%3D%5C+%5Ctextgreater+%5C+x_1%3D1%2B%5Cfrac%7B5%5Cpi%7D%7B4%7D%2B2%5Cpi+n%2C+n%5Cin+Z%5C%5C%0Ax_2-1%3D%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B2%5Cpi+k%2C+k%5Cin+Z+%3D%5C+%5Ctextgreater+%5C++x_2%3D1%2B%5Cfrac%7B7%5Cpi%7D%7B4%7D%2B2%5Cpi+k%2C+k%5Cin+Z)
А потом решаем неравенства: 0 <= x_1 <=2pi и 0<=x_2<=2pi, находим целые n и k, подставляем в формулу соответствующего корня
1)
-8ху +4у - 4х + 2х +8ху=4у - 2х
при х=4,4 и у=10,3
4*10,3-2*4,4= 41,2 - 8,8 = 32,4
Ответ:32,4.
2) -2х-4,3 = - 0,5
-2х = -0,5 +4,3
-2х=3,8
х= 3,8/(-2)
х= - 1,9
Ответ:х= - 1,9
![\left \{ {{x-2y=0} \atop {5xy+y^2=44}} \right. \left \{ {{x=2y} \atop {5xy+y^2=44}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7Bx-2y%3D0%7D+%5Catop+%7B5xy%2By%5E2%3D44%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7Bx%3D2y%7D+%5Catop+%7B5xy%2By%5E2%3D44%7D%7D+%5Cright.)
Подставим первое уравнение во второе и отдельно его решим
![5(2y)y+y^2=44 \\ 10y^2+y^2=44 \\ 11y^2=44|:11 \\ y^2=4 \\ y=\sqrt{4} \\ y=+-2](https://tex.z-dn.net/?f=5%282y%29y%2By%5E2%3D44+%5C%5C+10y%5E2%2By%5E2%3D44+%5C%5C+11y%5E2%3D44%7C%3A11+%5C%5C+y%5E2%3D4+%5C%5C+y%3D%5Csqrt%7B4%7D+%5C%5C+y%3D%2B-2+)
Вернемся в систему которых теперь будет две
![1. \left \{ {{x=2y} \atop {y=2}} \right. \left \{ {{x=2*2} \atop {y=2}} \right. \left \{ {{x=4} \atop {y=2}} \right. \\2. \left \{ {{x=2y} \atop {y=-2}} \right. \left \{ {{x=2*(-2)} \atop {y=-2}} \right. \left \{ {{x=-4} \atop {y=-2}} \right.](https://tex.z-dn.net/?f=1.+%5Cleft+%5C%7B+%7B%7Bx%3D2y%7D+%5Catop+%7By%3D2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D2%2A2%7D+%5Catop+%7By%3D2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D4%7D+%5Catop+%7By%3D2%7D%7D+%5Cright.+%5C%5C2.+%5Cleft+%5C%7B+%7B%7Bx%3D2y%7D+%5Catop+%7By%3D-2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D2%2A%28-2%29%7D+%5Catop+%7By%3D-2%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7Bx%3D-4%7D+%5Catop+%7By%3D-2%7D%7D+%5Cright.+)
Ответ(4:2) и (-4:-2)
p⁴-2p²q+q²=(p²-q)²
формула сокращённого умножения, квадрат разности ((a-b)²=a²-2ab+b²)