已知f(α)=sin(π/2+α)cos(11π/2-α)/cos(-π-α)sin(9π/2-α)(1)化简f(α)(2)若α是第三象限的角，且sin(α-7π/2)=-1/2,求f(α)的值(3)若α=-25π/6,求f(α)的值

Question

已知f(α)=sin(π/2+α)cos(11π/2-α)/cos(-π-α)sin(9π/2-α)
(1)化简f(α)
(2)若α是第三象限的角，且sin(α-7π/2)=-1/2,求f(α)的值
(3)若α=-25π/6,求f(α)的值

Answer 1

f(α)=sin(π/2+α)cos(11π/2-α)/cos(-π-α)sin(9π/2-α)
=cosα(-sinα)/(-cosαcosα)
=tanα
sin(α-7π/2)=sin[-4π+π/2+α]=cosα=-1/2 ,α=4π/3 (α是第三象限的角)
f(α)=f(4π/3)=tan4π/3=√3
f(-25π/6)=tan(-25π/6)=-tan(25π/6)=-tan(4π+π/6)=-tanπ/6=-√3/3