Question

设向量a=(sinx,sinx),b=(cos,sinx),函数f(x)=a*(a-b),求f(x)的最大值,最小值

Answer 1

f(x)=a^2-ab

=(sinx)^2+(sinx)^2-sinxcosx-(sinx)^2

=(sinx)^2-sinxcosx

=(1/2)(1-cos2x)-(1/2)sin2x

= - (1/2)(sin2x+cos2x)+(1/2)

= - (√2/2)sin(2x+π/4)+(1/2)

f(max)=(1/2)+(√2/2)

f(min)=(1/2)-(√2/2)