已知α是第四象限角,且f(α)=sin(α-π/2)cos(3/2π+α)tan(π-α)/tan(-α-π)sin(-π-α)(1)化简f(α);(2)若cos(α-π/2)=-1/4,求f(α)

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已知α是第四象限角,且f(α)=sin(α-π/2)cos(3/2π+α)tan(π-α)/tan(-α-π)sin(-π-α)(1)化简f(α);(2)若cos(α-π/2)=-1/4,求f(α)已

已知α是第四象限角,且f(α)=sin(α-π/2)cos(3/2π+α)tan(π-α)/tan(-α-π)sin(-π-α)(1)化简f(α);(2)若cos(α-π/2)=-1/4,求f(α)
已知α是第四象限角,且f(α)=sin(α-π/2)cos(3/2π+α)tan(π-α)/tan(-α-π)sin(-π-α)
(1)化简f(α);
(2)若cos(α-π/2)=-1/4,求f(α)

已知α是第四象限角,且f(α)=sin(α-π/2)cos(3/2π+α)tan(π-α)/tan(-α-π)sin(-π-α)(1)化简f(α);(2)若cos(α-π/2)=-1/4,求f(α)
f(α)=sin(α-π/2)cos(3/2π+α)tan(π-α)/tan(-α-π)sin(-π-α)
= - cos(α)sin(α)( - tan(α)) / ( - tan(α))sin(α)
= - cos(α)
因为α是第四象限角,所以cos(α)为正
f(α)= - cos(α)= - 根号(1-sin^2(α))= - 根号(1-cos^2(α-π/2))= - 根号(1 - 1/16)
= - 根号15 / 4 (负四分之根号十五)