已知α是第三象限角,且f（a）=[sin(5π-α）cos（α+3π/2）cos（π+α）]/[sin（α-3π/2）cos（α+π/2）tan（α-3π）]1,化简f(a)2,已知cos(π-α)=1/5,求f(a)的值

Question

已知α是第三象限角,
且f（a）=[sin(5π-α）cos（α+3π/2）cos（π+α）]/[sin（α-3π/2）cos（α+π/2）tan（α-3π）]
1,化简f(a)
2,已知cos(π-α)=1/5,求f(a)的值

Answer 1

1）f(α)= [sin(5π-α)cos(α+3π/2)cos(π+α)]/[sin(α-3π/2)cos(α+π/2)tan(α-3π)]
= [cosαsinα(-cosα)]/[cosα(-sinα)tanα]
= cotαcosα
2）cos(π-α) = -cosα = 1/5,cosα = -1/5
又α是第三象限角
所以sinα = -2√6/5,cotα = cosα/sinα = √6/12
f(α) = √6/12·(-1/5) = -√6/60