Question

已知函数f(x)=sinx^2-acos(π/2-x)+1/2a,x∈[-π/6,5π/6],记f（x）的最小值为g（a

Answer 1

1.根据诱导公式cos(π/2-x)=sinx,则f(x)=sinx^2-asinx+1/2a.

2.f(x)变形为：f(x)=(sinx-1/2*a)^2-1/4*a+1/2a.

3.a为常数,-1/4*a+1/2a是一个固定的常数,要想使有最小值,则(sinx-1/2*a)^2=0,即sinx=1/2*a,x∈[-π/6,5π/6],-1/2=