已知f(a)=sin(π-a)cos(2π-a)tan(-π+3π/2)/tan(π/2)sin(-π-a)若a是第三象限角且cos(a-3π/2)=1/5求f
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![已知f(a)=sin(π-a)cos(2π-a)tan(-π+3π/2)/tan(π/2)sin(-π-a)若a是第三象限角且cos(a-3π/2)=1/5求f](/uploads/image/z/581783-23-3.jpg?t=%E5%B7%B2%E7%9F%A5f%28a%29%3Dsin%28%CF%80-a%29cos%282%CF%80-a%29tan%28-%CF%80%2B3%CF%80%2F2%29%2Ftan%28%CF%80%2F2%29sin%28-%CF%80-a%29%E8%8B%A5a%E6%98%AF%E7%AC%AC%E4%B8%89%E8%B1%A1%E9%99%90%E8%A7%92%E4%B8%94cos%28a-3%CF%80%2F2%29%3D1%2F5%E6%B1%82f)
已知f(a)=sin(π-a)cos(2π-a)tan(-π+3π/2)/tan(π/2)sin(-π-a)若a是第三象限角且cos(a-3π/2)=1/5求f
已知f(a)=sin(π-a)cos(2π-a)tan(-π+3π/2)/tan(π/2)sin(-π-a)若a是第三象限角且cos(a-3π/2)=1/5求f
已知f(a)=sin(π-a)cos(2π-a)tan(-π+3π/2)/tan(π/2)sin(-π-a)若a是第三象限角且cos(a-3π/2)=1/5求f
a是第三象限角
cos(a-3π/2)=1/5
cos(a-3π/2)=cos(-2π+(π/2+a))=cos(π/2+a)=cos(π-(π/2-a))=-cos(π/2-a)=-sina=1/5
sina=-1/5
cosa=-根号(1-sin^2a)=-2根号6 /5
f(a)=sin(π-a)cos(2π-a)tan(-π+3π/2) / {tan(π/2)sin(-π-a)}
=sinacosa tan(-π+π+π/2) / {tan(π/2)[-sin(-a)]}
=sinacosa tan(π/2) / {tan(π/2)sina}
=cosa
=-2根号6 /5
f(a)=sin(π-a)cos(2π-a)tan(-π+3π/2)/tan(π/2)sin(-π-a)
=sina cosa tan(π/2)/tan(π/2)sina
=cos a
cos(a-3π/2)=cos (a-3π/2)+2π=cos π/2+a=-sina=1/5
因为a是第三象限角
f(a)=cos a= -√(1-sin^2)=-2√6/5