Question

第13题。__

Answer 1

f(α)= sin(α-3π)cos(2π-α)sin(3π/2-α)/[cos(-2π-α)sin(-π-α)]
=-sin(2π+π-α)cosαsin(π+π/2-α)/[-cos(2π+α)sin(π+α)]
=sin(π-α)cosα[-sin(π/2-α)]/[cosα(-sinα)]
=sinαsin(π/2-α)/sinα
=sin(π/2-α)
=cosα
(1) f(31π/3)=f(10π+π/3)=cosπ/3=1/2
(2) β=α+π/2+2π 或 β=α-π/2+2π
f(β)=f(α+π/2+2π)=cos(α+π/2+2π)=-sinα
或 f(β)=f(α-π/2+2π)=cos(α-π/2+2π)=cos(π/2-α)=sinα
(3) f²(α)+f(α)=cos²α+cosα=(cosα+1/2)²-1/4
当 α=2π/3时 有最小值：-1/4
则范围为：【-1/4，2）