设函数f(x)=sin(1/2x+φ)(0

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设函数f(x)=sin(1/2x+φ)(0
设函数f(x)=sin(1/2x+φ)(0

设函数f(x)=sin(1/2x+φ)(0
因为y=f(x)图像的一条对称轴是直线x=∏/4
所以f(π/4)等于1或-1
因为1/2*π/4+φ=π/8+φ,且0

（1）
∵对称轴1/2x+φ=π/2+kπ
∴x=π+2kπ-2φ
∵对称轴x=π/4
∴π/4=π+2kπ-2φ
∴φ=3π/8+kπ
∵0﹤φ﹤π/2
∴φ=3π/8
(2)
∵f(x)=sin(1/2x+3π/8)

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（1）
∵对称轴1/2x+φ=π/2+kπ
∴x=π+2kπ-2φ
∵对称轴x=π/4
∴π/4=π+2kπ-2φ
∴φ=3π/8+kπ
∵0﹤φ﹤π/2
∴φ=3π/8
(2)
∵f(x)=sin(1/2x+3π/8)
∴-π/2﹤1/2x+3π/8﹤π/2
∴-7π/4﹤x﹤π/4
∴单调增区间为（-7π/4，π/4）

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