已知sinα=3/5,α∈(π/2,π)求sin(α-π/4).cos(α+π/3)及tan2π的值

题目

已知sinα=3/5,α∈(π/2,π)求sin(α-π/4).cos(α+π/3)及tan2π的值

答案

sinα=3/5,α∈(π/2,π)
得：cosα=-4/5 tanα=-3/4
sin(α-π/4)=sinαcosπ/4-sinπ/4cosα=(7√2)/10
cos(α+π/3)=cosαcosπ/3-sinαsinπ/3=(-4-3√3)/10
tan2α=（-2*3/4）/(1-(-3/4)^2)=-24/7