f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0_数学解答

f(x)=1/2sin2xsinψ+COS²xcosψ-1/2sin(π/2+ψ),(0<ψ<π)其图像过点(π/6,1/2)求ψ

人气：472 ℃　时间：2019-10-24 05:37:34

解答

f(π/6)=√3/4sinψ+3/4cosψ-1/2cosψ
=√3/4sinψ+1/4cosψ
=1/2(√3/2sinψ+1/2cosψ)
=1/2sin(ψ+π/6)
=1/2
sin(ψ+π/6)=1
ψ+π/6=2kπ+π/2
ψ=2kπ+π/3,k∈Z