已知α是第四象限角,且f(α)=sin(π-α)*cos(2π-α)*tan(-α+3π/2)/cos(-α-π),(1)化简f(a).(2)若cos(a-3π/2)=1/5,求f(a)的值.(3)若a=1860°,求f(a)的值.
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![已知α是第四象限角,且f(α)=sin(π-α)*cos(2π-α)*tan(-α+3π/2)/cos(-α-π),(1)化简f(a).(2)若cos(a-3π/2)=1/5,求f(a)的值.(3)若a=1860°,求f(a)的值.](/uploads/image/z/1596564-36-4.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%E6%98%AF%E7%AC%AC%E5%9B%9B%E8%B1%A1%E9%99%90%E8%A7%92%2C%E4%B8%94f%28%CE%B1%29%3Dsin%28%CF%80-%CE%B1%29%2Acos%282%CF%80-%CE%B1%29%2Atan%28-%CE%B1%2B3%CF%80%2F2%29%2Fcos%28-%CE%B1-%CF%80%29%2C%EF%BC%881%EF%BC%89%E5%8C%96%E7%AE%80f%EF%BC%88a%EF%BC%89.%EF%BC%882%EF%BC%89%E8%8B%A5cos%EF%BC%88a-3%CF%80%2F2%EF%BC%89%3D1%2F5%2C%E6%B1%82f%EF%BC%88a%EF%BC%89%E7%9A%84%E5%80%BC.%EF%BC%883%EF%BC%89%E8%8B%A5a%3D1860%C2%B0%2C%E6%B1%82f%EF%BC%88a%EF%BC%89%E7%9A%84%E5%80%BC.)
已知α是第四象限角,且f(α)=sin(π-α)*cos(2π-α)*tan(-α+3π/2)/cos(-α-π),(1)化简f(a).(2)若cos(a-3π/2)=1/5,求f(a)的值.(3)若a=1860°,求f(a)的值.
已知α是第四象限角,且f(α)=sin(π-α)*cos(2π-α)*tan(-α+3π/2)/cos(-α-π),(1)化简f(a).
(2)若cos(a-3π/2)=1/5,求f(a)的值.(3)若a=1860°,求f(a)的值.
已知α是第四象限角,且f(α)=sin(π-α)*cos(2π-α)*tan(-α+3π/2)/cos(-α-π),(1)化简f(a).(2)若cos(a-3π/2)=1/5,求f(a)的值.(3)若a=1860°,求f(a)的值.
f(α)=sin(π-α)*cos(2π-α)*tan(-α+3π/2)/cos(-α-π)
=-sin(α)*cos(α)*cot(α)/cos(α)
=-sin(α)**cot(α)
=-cosα
2若cos(a-3π/2)=1/5
即sinα=-1/5
即cosα=2√6/5或cosα=-2√6/5
即f(a)=-cosα=2√6/5或=-2√6/5
3 a=1860°,求f(a)=-cos1860°
=-cos60°=-1/2
答:
(1)f(α)=sin(π-α)*cos(2π-α)*tan(-α+3π/2)/cos(-α-π)
=sinα*cosα*cotα/-cosα=-cosα
(2)cos(a-3π/2)=1/5 → -sinα=1/5;α是第四象限角 cosα=2√ 6/5
f(α)=-2√ 6/5
(3)α=1860°=5*2π+π/3,
f(α)=-cosπ/3=-1/2