求1/2[√2sin(2x-π/4)+1]在区间[π/8,3π/4]上的取值范围,
问题描述:
求1/2[√2sin(2x-π/4)+1]在区间[π/8,3π/4]上的取值范围,
答
x∈[π/8,3π/4]
2x∈[π/4,3π/2]
2x-π/4∈[0,5π/4]
2sin(2x-π/4)∈[-√2/2,1]
[√2sin(2x-π/4)+1]/2∈[ 0,(√2+1)/2 ]