Question

高一三角函数 函数 y=sin^4x-sinxcosx+cos^4x x∈R的值域是集合_____

Answer 1

解;y=sin^4x-sinxcosx+cos^4x =
y=(sin^2x+cos^2x)^2-sinxcosx-2sin^2xcos^2x
=1-1/2sin2x-1/2(sin2x)^2
因为-1<=sin2x<=1
所以0<=y<=9/8
即所求为{y|0<=y<=9/8}