Question

已知函数f(x)=1/2sin2xcosφ+sin²xsinφ+……

Answer 1

（1）解析：∵函数f(x)=1/2sin2xcosφ+(sinx)^2sinφ+1/2cos(π/2+φ)+1/2
=1/2sin2xcosφ+1/2(1-cos2x)sinφ-1/2sinφ+1/2
=1/2sin2xcosφ-1/2cos2xsinφ+1/2
=1/2sin(2x-φ)+1/2
∵其图像过点(π/6,1)
f(π/6)=1/2sin(π/3-φ)+1/2=1==>sin(π/3-φ)=1==>φ=-π/6
∴f(x)=1/2sin(2x+π/6)+1/2
其对称中心为：2x+π/6=kπ==>x=kπ/2-π/12==>(kπ/2-π/12,1/2)
（2）解析：将f(x)图像
Y坐标不变，X坐标扩大2倍，得y=1/2sin(x+π/6)+1/2
X坐标不变，Y坐标扩大2倍，得到g(x)=sin(x+π/6)+1

∵在区间[0,π/2]上
单调增区间：2kπ-π/2<=x+π/6<=2kπ+π/2==>2kπ-2π/3<=x<=2kπ+π/3
g(0)=sin(π/6)+1=3/2
g(π/2)=sin(π/2+π/6)+1=1+√3/2
∴g(x)在区间[0, π/2]上最大值为2，最小值为3/2

Answer 2

太难了吧，你理科的吧

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