已知α是第三象限角,且f(α)=sin(π-α)cos(2π-α)sin(3π2-α)sin(α-π)cos(-α-π)sin(-π-α)cos(3π2-α)(1)化简f(α);(2)若cos(α-3

题目简介

已知α是第三象限角,且f(α)=sin(π-α)cos(2π-α)sin(3π2-α)sin(α-π)cos(-α-π)sin(-π-α)cos(3π2-α)(1)化简f(α);(2)若cos(α-3

题目详情

已知α是第三象限角,且f(α)=
sin(π-α)cos(2π-α)sin(
2
-α)sin(α-π)
cos(-α-π)sin(-π-α)cos(
2
-α)

(1)化简f(α);
(2)若cos(α-
2
)=
1
5
,求f(α)的值;
(3)若α=-1860°,求f(α)的值.
题型:解答题难度:中档来源:不详

答案

(1)f(α)=
sin2αcos2α
cosαsin2α
=cosα;
(2)∵α为第三象限角,∴sinα<0,
∵cos(α-class="stub"3π
2
)=-sinα=class="stub"1
5
,即sinα=-class="stub"1
5

∴cosα=-
2
6
5

则f(α)=cosα=-
2
6
5

(3)将α=-1860°代入得:f(α)=cosα=cos(-1860°)=cos1860°=cos(5×360°+60°)=cos60°=class="stub"1
2

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