Question

求函数y=2sin^2x+2cosx-3的值域

Answer 1

y=2sin^2x+2cosx-3

=2-2cos^2x+2cosx-3

=-2cos^2x+2cosx-1

=-2(cosx-1/2)^2-1/2

因为-1≤cosx≤1,

所以cosx=1/2时,函数取到最大值-1/2,

cosx=-1时,函数取到最小值-5,

∴函数值域是[-5,-1/2].