已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4)的值
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![已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4)的值](/uploads/image/z/2832835-67-5.jpg?t=%E5%B7%B2%E7%9F%A5sin%28x-y%29cosx-cos%28y-x%29sinx%3D3%E5%88%86%E4%B9%8B5%2Cy%E6%98%AF%E7%AC%AC%E4%B8%89%E8%B1%A1%E9%99%90%E8%A7%92%2C%E6%B1%82sin%28y%2B5%CF%80%E5%88%86%E4%B9%8B4%EF%BC%89%E7%9A%84%E5%80%BC)
已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4)的值
已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4)的值
已知sin(x-y)cosx-cos(y-x)sinx=3分之5,y是第三象限角,求sin(y+5π分之4)的值
7√2/10
详情见
sin(x-y)cosx-cos(y-x)sinx=3/5,
即sin(x-y)cosx-cos(x-y)sinx=3/5,
sin[(x-y)-x] =3/5,
sin(-y)= 3/5,
siny= -3/5.
y是第三象限角,所以cosy=-4/5.
sin(y+5π/4)=-sin(y+π/4)
=-(sin y cosπ/4+cos y sinπ/4)
=7√2/10.
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