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.
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