Question

已知函数 f(x)=根号3sinxcosx+cos的平方x-1/2

Answer 1

f(x)=√3sinxcosx+cos?x

=√3/2sin2x+(cos2x+1)/2

=√3/2sin2x+1/2cos2x+1/2

=sin(2x+π/6)+1/2

f(x)的最小正周期为2π/2=π

∵x∈R

∴由三角函数有界性可知,

恒有:-1≤sin[2x-(π/6)]≤1

∴-2≤sin[2x-(π/6)]-1≤0

即恒有:-2≤f(x)≤0

∴最小值f(x)min=-2