已知α是第三象限角,且f(α)=[sin(π+α)cos(2π-α)tan(-α+3π/2)tan(-α-π)]/sin
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已知α是第三象限角,且f(α)=[sin(π+α)cos(2π-α)tan(-α+3π/2)tan(-α-π)]/sin(π-α)
(1)化简 (2)cos(α-3π/2)=3/5,求f(α)的值 (3)若α=-1860°,求f(α)的值
(1)化简 (2)cos(α-3π/2)=3/5,求f(α)的值 (3)若α=-1860°,求f(α)的值
(1)f(α)=[sin(π+α)cos(2π-α)tan(-α+3π/2)tan(-α-π)]/sin(π-α)
=[(-sinα)*cosα*cotα*(-tanα)]/sinα
=cosα;
(2)∵cos(α-3π/2)=3/5 ==>cos(3π/2-α)=3/5
==>-sinα=3/5
∴sinα=-3/5
∵α是第三象限角
∴cosα
=[(-sinα)*cosα*cotα*(-tanα)]/sinα
=cosα;
(2)∵cos(α-3π/2)=3/5 ==>cos(3π/2-α)=3/5
==>-sinα=3/5
∴sinα=-3/5
∵α是第三象限角
∴cosα
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