Question

已知函数f(x)=acos2(平方)x+bsinxcosx,且f(0)=f(π/3)=2

Answer 1

1.f(x)=a（cosx)^2+bsinxcosx,f(0)=f(π/3)=2,

∴a=2,

1/2+b√3/4=2,b=2√3,

∴f(x)=1+cos2x+√3sin2x=1+2sin(2x+π/6）,

它的增区间由(2k-1/2)π=0,k>=0,或k=0,或k