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](/uploads/image/z/2496816-0-6.jpg?t=%E5%B7%B2%E7%9F%A5f%28x%29%3D%28sin%28%CF%80-x%29%2Acos%282%CF%80-x%29%29%2Fcos%28-%CF%80-x%29%2Atan%28%CF%80-x%29%2C%E5%88%99f%28-31%CF%80%2F3%29%E7%9A%84%E5%80%BC%E4%B8%BA)
已知f(x)=(sin(π-x)*cos(2π-x))/cos(-π-x)*tan(π-x),则f(-31π/3)的值为
已知f(x)=(sin(π-x)*cos(2π-x))/cos(-π-x)*tan(π-x),则f(-31π/3)的值为
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
首先,该函数为周期函数,周期为2π,因此f(-31π/3)=f(-π/3)
代入,自己计算一下!