Question

函数f(x)=2sinxcos(x+6分之拍)-cos2x+m（1）求它的最小正周期,

Answer 1

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