已知sin(2x-π/4)=1/2,求x的取值范围,

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已知sin(2x-π/4)=1/2,求x的取值范围,

已知sin(2x-π/4)=1/2,求x的取值范围,
已知sin(2x-π/4)=1/2,求x的取值范围,

已知sin(2x-π/4)=1/2,求x的取值范围,
2x-π/4=π/6+2kπ
2x=5π/12+2kπ
x=5π/24+kπ k属于Z
2x-π/4=5π/6+2kπ
2x=13π/12+2kπ
x=13π/24+kπ k属于Z

sin(2x-π/4)=1/2
2x-π/4=2kπ+π/6或2x-π/4=2kπ+5π/6 (k∈Z)
x=kπ+5π/24或x=kπ+13π/24 (k∈Z)

设2x-π/4=t,sint=0.5,得t=π/6±2π或5π/6±2π,即2x-π/4=π/6±2π或5π/6±2π,解得x=5π/6±2π或13π/24±π