1)=sin3x+3=sin4x
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А4)А-3 Б-1 В-4
Б1) точки пересечения функций (4;6)
Б2) y=3-1,5x y=-6
-6=3-1,5x
-6-3+1,5x=0
-9+1,5x=0
1,5x=9
x=6
По теореме синусов
![\frac{a}{sina}=2R](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsina%7D%3D2R)
, найдем любой из углов
![\frac{20}{sina}=2R\\ sina=\frac{20}{2R}=\frac{20}{\frac{65}{3}}=\frac{60}{65}=\frac{12}{13}\\ ](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7Bsina%7D%3D2R%5C%5C%0Asina%3D%5Cfrac%7B20%7D%7B2R%7D%3D%5Cfrac%7B20%7D%7B%5Cfrac%7B65%7D%7B3%7D%7D%3D%5Cfrac%7B60%7D%7B65%7D%3D%5Cfrac%7B12%7D%7B13%7D%5C%5C%0A)
это острый угол, второй угол
![\frac{13}{sinb}=2R\\ sinb=\frac{13}{\frac{65}{3}}\\ sinb=\frac{39}{65}=\frac{3}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7Bsinb%7D%3D2R%5C%5C%0Asinb%3D%5Cfrac%7B13%7D%7B%5Cfrac%7B65%7D%7B3%7D%7D%5C%5C%0Asinb%3D%5Cfrac%7B39%7D%7B65%7D%3D%5Cfrac%7B3%7D%7B5%7D)
это тоже острый угол. Обозначим за
![x](https://tex.z-dn.net/?f=x)
третью сторону , и согласно теореме косинусов получаем
![20^2=13^2+x^2-26*x*cosa\\ sina=\frac{12}{13}\\ cosa=\sqrt{1-(\frac{12}{13})^2}=\sqrt{\frac{25}{169}}=\frac{5}{13}\\ 400=169+x^2-26x*\frac{5}{13}\\ 400=169+x^2-10x\\ x^2-10x-231=0\\ (x-21)(x+11)=0\\ x=21](https://tex.z-dn.net/?f=20%5E2%3D13%5E2%2Bx%5E2-26%2Ax%2Acosa%5C%5C%0Asina%3D%5Cfrac%7B12%7D%7B13%7D%5C%5C%0Acosa%3D%5Csqrt%7B1-%28%5Cfrac%7B12%7D%7B13%7D%29%5E2%7D%3D%5Csqrt%7B%5Cfrac%7B25%7D%7B169%7D%7D%3D%5Cfrac%7B5%7D%7B13%7D%5C%5C%0A400%3D169%2Bx%5E2-26x%2A%5Cfrac%7B5%7D%7B13%7D%5C%5C%0A400%3D169%2Bx%5E2-10x%5C%5C%0Ax%5E2-10x-231%3D0%5C%5C%0A%28x-21%29%28x%2B11%29%3D0%5C%5C%0Ax%3D21)
Ответ 21
2sinx-1≠0
2sinx≠1
sinx≠1/2
x≠π/3+2πn U x≠2π/3+2πn,n∈z
x∈[2πn;π/3+2πn) U (π/3+2πn;2π/3+2πn) U (2π/3+2πn;2π+2πn],n∈z