已知α是第三象限的角,且f(α)=sin(π−α)cos(2π−α)tan(3π2−α)cos(−π−α).
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已知α是第三象限的角,且f(α)=
sin(π−α)cos(2π−α)tan(
| ||
cos(−π−α) |
(1)化简可得f(α)=
sinαcosαsin(
3π
2−α)
−cosαcos(
3π
2−α)
=
sinαcosα(−cosα)
−cosα(−sinα)=-cosα;
(2)∵cos(α-
3π
2)=
1
5,∴由诱导公式可得-cosα=
1
5
∴f(α)=-cosα=
1
5;
(3)当α=-1860°时,f(α)=-cos(-1860°)
=-cos(1860°)=-cos(5×360°+60°)
=-cos60°=−
1
2
sinαcosαsin(
3π
2−α)
−cosαcos(
3π
2−α)
=
sinαcosα(−cosα)
−cosα(−sinα)=-cosα;
(2)∵cos(α-
3π
2)=
1
5,∴由诱导公式可得-cosα=
1
5
∴f(α)=-cosα=
1
5;
(3)当α=-1860°时,f(α)=-cos(-1860°)
=-cos(1860°)=-cos(5×360°+60°)
=-cos60°=−
1
2
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