函数f(x)=sin(2x+φ)((|φ|

来源：学生作业帮助网编辑：作业帮时间：2024/05/07 07:17:40

函数f(x)=sin(2x+φ)((|φ|
函数f(x)=sin(2x+φ)((|φ|

f(x)=sin(2x+a)
向左平移π/6
f(x)=sin(2x+π/3+a)
因为f(x)=sin2x 是奇函数所以π/3+a=0 所以a=-π/3
f(x)=sin(2x-π/3)
0<=x<=π/2
-π/3<=2x-π/3<=2π/3
所以当x=0时取到最小值-根号3/2

sin(2(x+π/6)+φ) = sin2x
φ = -π/3

f(0) = -sinπ/3
f(π/2) = sin2π/3
最小值f(0) = -根号（3）/2

平移后f(x)=sin(2x+3/π+φ) 又因为(|φ|<π/2) 且为奇函数所以φ=-π/3
所以f(x)=sin（2x-π/3）
因为x∈【0，π/2】
所以2x-π/3∈【-π/3，2π/3】
所以f(x)min=sin(-π/3)=-根3/2

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