cosα等于-4/5,α是第三项的角求sin(3π/4-α),cos(π/4+2α)的值
问题描述:
cosα等于-4/5,α是第三项的角求sin(3π/4-α),cos(π/4+2α)的值
答
sinα=-3/5,cos2α=7/25,sin2α=24/25
sin(3π/4-α)=sin3(π/4)cosα-cos(3π/4)sina=-(7√2)/20
cos(π/4+2α)=cos(π/4)cos2α-sin(π/4)sin2α=√2/2*7/25-√2/2*24/25=-(17√2)/50
长度限制
答
cosα=-4/5,α是第三象限的角
sinα=-3/5
cos2α=2cosα*cosα-1=7/25
sin2α=2sinαcosα=24/25
sin(3π/4-α)=sin3π/4*cosα-cos3π/4*sinα=-7√2/10
cos(π/4+2α)=cosπ/4*cos2α-sinπ/4*sin2α=-17√2/50