已知f(x)=(sin(π-x)*cos(2π-x))/cos(-π-x)*tan(π-x),则f(-31π/3)的值为
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已知f(x)=(sin(π-x)*cos(2π-x))/cos(-π-x)*tan(π-x),则f(-31π/3)的值为
f(x)=(sin(π-x)*cos(2π-x))/cos(-π-x)*tan(π-x)
=(sin(π-x)*cosx)/(cos(-π-x+2π)*tan(π-x)
=(sin(π-x)*cosx)/(cos(π-x)*tan(π-x)
=tan(π-x)*cosx)/tan(π-x)
=cosx
f(x)是周期函数,偶函数则周期为2π
f(-31π/3)=f(31π/3)
=f(1π/3+2π*5)
=f(1π/3)
=1/2
=(sin(π-x)*cosx)/(cos(-π-x+2π)*tan(π-x)
=(sin(π-x)*cosx)/(cos(π-x)*tan(π-x)
=tan(π-x)*cosx)/tan(π-x)
=cosx
f(x)是周期函数,偶函数则周期为2π
f(-31π/3)=f(31π/3)
=f(1π/3+2π*5)
=f(1π/3)
=1/2
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