已知α为第三象限角,且f(α)=sin(π-α)cos(2π-α)tan(-α+π)/sin(π+α)tan(2π-α)
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已知α为第三象限角,且f(α)=sin(π-α)cos(2π-α)tan(-α+π)/sin(π+α)tan(2π-α)
1)化简f(α) (2)cos(α-3π/2)=1/5,求f(α)的值 (3)若α=1920°,求f(α)的值
1)化简f(α) (2)cos(α-3π/2)=1/5,求f(α)的值 (3)若α=1920°,求f(α)的值
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f(α)=sin(π-α)cos(2π-α)tan(-α+π)/sin(π+α)tan(2π-α)
=sinacosa(-tana)/(-sina)(-tana)
=-(sinacosatana/sinatana)
=cosa
cos(α-3π/2)=1/5
=cosacos3π/2+sinasin3π/2
=-sina=1/5
sina=-1/5
a在第三象限
cosa=负的五分之二倍根六
a=1920°
cos1920°=cos(11π-60°)=cos(π-60°)=-cos60°=-1/2
=sinacosa(-tana)/(-sina)(-tana)
=-(sinacosatana/sinatana)
=cosa
cos(α-3π/2)=1/5
=cosacos3π/2+sinasin3π/2
=-sina=1/5
sina=-1/5
a在第三象限
cosa=负的五分之二倍根六
a=1920°
cos1920°=cos(11π-60°)=cos(π-60°)=-cos60°=-1/2
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