已知sin(θ-π/4)=-1/3,π<θ<3π/2,求cos2θ的值.要具体过程…

问题描述:

已知sin(θ-π/4)=-1/3,π<θ<3π/2,求cos2θ的值.
要具体过程…

sin(2*(θ-π/4))=-cos2θ

cos2(θ-π/4)=1-2[sin(θ-π/4)]^2=7/9
cos2(θ-π/4)=cos(2θ-π/2)=sin2θ
故sin2θ=8/9,[cos2θ]^2=1-(7/9)^2=32/81
π<θ<3π/2,3π/4<θ-π/4<5π/4,sin(θ-π/4)=-1/3