Question

已知f(a)=cos(-π-a)分之sin(π-a)cos(2π-a)tan(-a+2分之3π).则f(-3分之31π)

Answer 1

sin(π-α)=sinα,

cos(2π-α)=cosα

tan(-α+3π/2)=cotα=cosα/sinα,

cos(-π-α)=cos(π+α)=-cosα.

∴f(α)=-cosα,f(-31π/3)= -cos(-31π/3)= -cos(31π/3)= -cos(π/3+5·2π)= -cos(π/3)= -1/2.