Sin2x + 1 = Cosx + 2Sinx
Sin2x - 2Sinx + 1 - Cosx = 0
(2SinxCosx - 2Sinx) + (1 - Cosx) = 0
2Sinx(Cosx - 1) - (Cosx - 1) = 0
(Cosx - 1)(2Sinx - 1) = 0
![\left[\begin{array}{ccc}Cosx-1=0\\2Sinx-1=0\end{array}\right\\\\\\\left[\begin{array}{ccc}Cosx=1\\Sinx=\frac{1}{2} \end{array}\right\\\\\\\left[\begin{array}{ccc}x=2\pi n,n\in Z \\x=(-1)^{n}arcSin\frac{1}{2}+\pi n,n\in Z \end{array}\right\\\\\\\left[\begin{array}{ccc}x=2\pi n,n\jn Z \\x=(-1)^{n}\frac{\pi }{6}+\pi n,n\in Z \end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DCosx-1%3D0%5C%5C2Sinx-1%3D0%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7DCosx%3D1%5C%5CSinx%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%3D2%5Cpi%20n%2Cn%5Cin%20Z%20%5C%5Cx%3D%28-1%29%5E%7Bn%7DarcSin%5Cfrac%7B1%7D%7B2%7D%2B%5Cpi%20n%2Cn%5Cin%20Z%20%20%20%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%3D2%5Cpi%20n%2Cn%5Cjn%20Z%20%5C%5Cx%3D%28-1%29%5E%7Bn%7D%5Cfrac%7B%5Cpi%20%7D%7B6%7D%2B%5Cpi%20n%2Cn%5Cin%20Z%20%20%20%5Cend%7Barray%7D%5Cright)
-0.027^(-1/3) + (1/6)⁻¹ -3⁻¹ +5.5⁰=
= - (0.3³)^(-1/3) + 6 - (1/3) +1 =
= - 0.3⁻¹ + 7 - 1/3 =
= -10/3 - 1/3 +7 =
= -11/3 + 21/3 =
= 10/3 = 3 ¹/₃
Min f(x)= f(-4)=-128+48-36=-116