已知sin(θ-π/4)=-1/3,π＜θ＜3π/2,求cos2θ的值.

题目

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

答案

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