函数f(x)=2sinxcos(x+6分之拍)-cos2x+m(1)求它的最小正周期,
问题描述:
函数f(x)=2sinxcos(x+6分之拍)-cos2x+m(1)求它的最小正周期,
(2)当x属于[负4分之拍,4分之拍],f(x)的最小值为负3,求m的值.要把每一步都写出来,
答
f(x)=2sinxcos(x+6分之拍)-cos2x+m
=sin(2x+π/6)+sin(-π/6)-cos2x+m
=sin(2x+π/6)-sin(π/2-2x)-1/2+m
=sin(2x-π/6)+m-1/2
∴T=2π/2=π
x=-π/6时 函数值最小
令-1+m-12=-3得m=10