已知sin(π-α)cos(-α+3π/2)/cos(-π-α),且α为第三象限角1.化简f(α)2.若cos(α+π/2)=1/5,求f(α)的值
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![已知sin(π-α)cos(-α+3π/2)/cos(-π-α),且α为第三象限角1.化简f(α)2.若cos(α+π/2)=1/5,求f(α)的值](/uploads/image/z/1076014-46-4.jpg?t=%E5%B7%B2%E7%9F%A5sin%28%CF%80-%CE%B1%29cos%28-%CE%B1%2B3%CF%80%2F2%29%2Fcos%28-%CF%80-%CE%B1%29%2C%E4%B8%94%CE%B1%E4%B8%BA%E7%AC%AC%E4%B8%89%E8%B1%A1%E9%99%90%E8%A7%921.%E5%8C%96%E7%AE%80f%28%CE%B1%292.%E8%8B%A5cos%EF%BC%88%CE%B1%2B%CF%80%2F2%EF%BC%89%3D1%2F5%2C%E6%B1%82f%EF%BC%88%CE%B1%EF%BC%89%E7%9A%84%E5%80%BC)
已知sin(π-α)cos(-α+3π/2)/cos(-π-α),且α为第三象限角1.化简f(α)2.若cos(α+π/2)=1/5,求f(α)的值
已知sin(π-α)cos(-α+3π/2)/cos(-π-α),且α为第三象限角1.化简f(α)2.若cos(α+π/2)=1/5,求f(α)的值
已知sin(π-α)cos(-α+3π/2)/cos(-π-α),且α为第三象限角1.化简f(α)2.若cos(α+π/2)=1/5,求f(α)的值
f(α) = sin(π-α)cos(-α+3π/2)/cos(-π-α)
= sinα cos(-α+2π-π/2)/cos(π+α)
= sinα cos(α+π/2)/(-cosα)
= sinα (-sinα)/(-cosα)
= sin^2α/cosα
α为第三象限角
cos(α+π/2)=1/5
-sinα = 1/5
sinα = -1/5
cosα = -√(1-sin^2α) = -2√6/5
f(α) = sin^2α/cosα = (-1/5)^2 / (-2√6/5) = -√6/60