已知cos(θ-π/4)=-根号2/10,并且θ是第二象限的角,求sinθ的值

已知cos(θ-π/4)=-根号2/10,并且θ是第二象限的角,求sinθ的值
已知cos(θ-π/4)=-根号2/10,并且θ是第二象限的角,求sinθ的值

已知cos(θ-π/4)=-根号2/10,并且θ是第二象限的角,求sinθ的值
cos(θ-π/4)=-根号2/10
θ是第二象限的角
sin(θ-π/4)=根号{1-cos^2((θ-π/4)} = 7根号2/10
sin(θ-π/4)+cos(θ-π/4)=7根号2/10-根号2/10=3根号2/5
根号2(sin(θ-π/4)cosπ/4+cos(θ-π/4)sinπ/4)=3根号2/5
sin（θ-π/4+cosπ/4）= 3/5
sinθ= 3/5