Question

已知f（α）=[cos（a-3π/2）*sin（7π/2+a）]/sin（-a-π）

①化简f（a）
②若f（a）=1/3，求tana的值
③若f（π/6-a）=1/3，求f（5π/6+a）的值

Answer 1

解1：
f(α)=[cos(α-3π/2)sin(7π/2+α)]/sin(-α-π)
f(α)=[cos(3π/2-α)sin(2π+3π/2+α)]/[-sin(α+π)]
f(α)=-sin(α)(-cosα)/(-sinα)
f(α)=-cosα

解2：
f(α)=-cosα
cosα=-1/3
sinα=±√[1-(1/3)^2]
sinα=±(2√2)/3
tanα=sinα/cosα
tanα=±2√2

解3：
f(π/6-α)=1/3
f(5π/6+α)=-cos(5π/6+α)
f(5π/6+α)=-cos(-5π/6-α)
f(5π/6+α)=-cos(π+π/6-α)
f(5π/6+α)=cos(π/6-α)
f(5π/6+α)=-f(π/6-α)
f(5π/6+α)=-1/3