y=sin（x-6/π）cosx最小值是,及对应的x值

Question

y=sin（x-6/π）cosx 最小值是,及对应的x值

Answer 1

y=sin(x-π/6)cosx
=(sinxcosπ/6-cosxsinπ/6)cosx
=sinxcosxcosπ/6-cos²xsinπ/6
=1/2sin2xcosπ/6-1/2(cos2x+1)sinπ/6
=1/2(sin2xcosπ/6-cos2xsinπ/6)-1/2sinπ/6
=1/2sin(2x-π/6)-1/4
y最小=1/2×(-1)-1/4=-3/4
2x-π/6=2nπ-π/2
x=nπ-π/3