已知sin(π-α)=-根号3/5,α是第四象限角,则tan(3/2π+α)的值为

已知sin(π-α)=-根号3/5,α是第四象限角,则tan(3/2π+α)的值为

sin(π-α)=sinα=-√3/5
∵α是第四象限角
∴cosα﹥0
∴cosα=√(1-sin²α)
=√[1-(-√3/5)²]
=√(1-3/25)
=√(22/25)
=√22/5
tan(3/2π+α)=-cotα
=-cosα/sinα
=(-√22/5)/(-√3/5)
=√22/√3
=√66/3