Question

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

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