已知sinα=-3/5,α是第四象限角,求sin(π/4 -α),cos(π/4 +α),tan(α -π/4)的值

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已知sinα=-3/5,α是第四象限角,求sin(π/4 -α),cos(π/4 +α),tan(α -π/4)的值

已知sinα=-3/5,α是第四象限角,求sin(π/4 -α),cos(π/4 +α),tan(α -π/4)的值
已知sinα=-3/5,α是第四象限角,求sin(π/4 -α),cos(π/4 +α),tan(α -π/4)的值

已知sinα=-3/5,α是第四象限角,求sin(π/4 -α),cos(π/4 +α),tan(α -π/4)的值
sinα=-3/5,α是第四象限角,cosα=4/5,
sin(π/4 -α)=sin(π/4)cosα-cos(π/4)sinα
=√2/2*4/5-√2/2(-3/5)
=7√2/10.
cos(π/4 +α)=cos(π/4)cosα-sin(π/4)sinα
=(√2/2)(4/5)-(√2/2)*(-3/5)
=7√2/10,
tanα =-3/4
tan(α -π/4)=(tanα-tanπ/4)/(1+tanαtanπ/4)
=(-3/4-1)/(1-3/4)
=-7.

根据第四象限角,先求出cosα、tanα的值,然后再用公式就可以了