已知f=[sin(π-α)cos(2π-α)tan(-π-α)]/sin(-π-α),⑴化简f(a)、⑵若α是第三象限,且cos﹙α－3π/2且cos﹙α－3π/2﹚=1/5,求f（a）的值、⑶若α＝﹣1860°,求f(a)的值⑴-sinα ⑵ 1/5 ⑶根号3/2我要具体步骤.
问题描述：
已知f=[sin(π-α)cos(2π-α)tan(-π-α)]/sin(-π-α),⑴化简f(a)、⑵若α是第三象限,且cos﹙α－3π/2
且cos﹙α－3π/2﹚=1/5,求f（a）的值、⑶若α＝﹣1860°,求f(a)的值
⑴-sinα ⑵ 1/5 ⑶根号3/2
我要具体步骤.
答
⑴
f(α) = [sin(π-α)*cos(2π-α)*tan(-π-α)]/sin(-π-α)
= [sin(α)*cos(-α)*tan(-α)]/sin(α)
= cos(-α)*tan(-α)
= cos(-α) * tan(-α)
= sin(-α)
= -sin(α)
⑵
cos﹙α - 3π/2﹚=cos﹙-2π + π/2 + α ﹚= cos(π/2 + α) = -sin(α) =1/5
∴ f(α) = -sin(α) = 1/5
⑶
f(α) = -sin(α) = -sin(-1860°) = -sin(-5×360°- 60°) = -sin(-60°) = sin60°= √3/2
答
⑴f(α) = [sin(π-α)cos(2π-α)tan(-π-α)]/sin(-π-α)= [sin(α)cos(-α)tan(-α)]/sin(α)= cos(-α)tan(-α)= cos(-α) * sin(-α) / cos(-α)= sin(-α)= -sin(α)⑵cos﹙α - 3π/2﹚=cos﹙-2π + π/2 + ...