已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?
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![已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?](/uploads/image/z/1043547-51-7.jpg?t=%E5%B7%B2%E7%9F%A5cos%EF%BC%88x-y%EF%BC%89cosx%2Bsin%EF%BC%88x%2By%EF%BC%89sinx%3Dm.%E4%B8%94y%E4%B8%BA%E7%AC%AC%E4%B8%89%E8%B1%A1%E9%99%90%E8%A7%92%2C%E6%B1%82siny%3F)
已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?
已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?
已知cos(x-y)cosx+sin(x+y)sinx=m.且y为第三象限角,求siny?
cos(x-y)=cosxcosy-sinxsiny sin(x+y)=sinxcosy+cosxsiny
上式左边=(cosx)^2cosy-sinxcosxsiny+(sinx)^2cosy+sinxcosxsiny
=cosy=m
所以,siny=+-(1-m^2)^(1/2) 因为y为第三象限角,所以siny为负
所以,siny=-(1-m^2)^(1/2)
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