Question

已知函数f(x)=1/2 sin2xsinφ+cos^2xcosφ-1/2sin(π/2+φ)（0＜φ＜π）图像过点(π

Answer 1

1、f(x) = 1/2 sin2x sinφ + (1+cos2x)/2 cosφ - 1/2 cosφ

= 1/2 sin2x sinφ + 1/2 cos2x cosφ = 1/2 cos(2x-φ)

f(π/6) = 1/2

cos(π/3 - φ) = 1又（0＜φ＜π）

所以φ = π//3

2、g(x)=1/2cos(4x-π/3)

当4x-π/3=0即x=π/12时取最大值1/2

当x=π/4时取最小值-1/4