已知sina=-3/5,a是第四象限角,求sin(π/4-a),cos(π/4+a),tan(a-π/4)的值
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![已知sina=-3/5,a是第四象限角,求sin(π/4-a),cos(π/4+a),tan(a-π/4)的值](/uploads/image/z/561744-0-4.jpg?t=%E5%B7%B2%E7%9F%A5sina%3D-3%2F5%2Ca%E6%98%AF%E7%AC%AC%E5%9B%9B%E8%B1%A1%E9%99%90%E8%A7%92%2C%E6%B1%82sin%28%CF%80%2F4-a%29%2Ccos%28%CF%80%2F4%2Ba%29%2Ctan%28a-%CF%80%2F4%29%E7%9A%84%E5%80%BC)
已知sina=-3/5,a是第四象限角,求sin(π/4-a),cos(π/4+a),tan(a-π/4)的值
已知sina=-3/5,a是第四象限角,求sin(π/4-a),cos(π/4+a),tan(a-π/4)的值
已知sina=-3/5,a是第四象限角,求sin(π/4-a),cos(π/4+a),tan(a-π/4)的值
a是第四象限角,cosa=4/5,tana=-3/4
sin(π/4-a)=sinπ/4cosa-cosπ/4sina=7√2/10
cos(π/4+a)=cosπ/4cosa-sinπ/4sina=7√2/10
tan(a-π/4)=(tana-tanπ/4)/(1+tanatanπ/4)=-7
解:cosa=4/5
原式=sin45度cosa-cos45度sina
=根号下2/2*4/5+根号下2/2*3/5
=8/5*根号下2/2
sina=-3/5,且a是第四象限角,所以cosa=4/5,tana=-3/4,(sinπ/4=√2/2,cosπ/4=√2/2,tanπ/4=1)
sin(π/4-a)
=sinπ/4·cosa-cosπ/4·sina
=√2/2·4/5-√2/2·(-3/5)
=√2/10
同理,可算出cos(π/4+a)=(7√2)/10
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sina=-3/5,且a是第四象限角,所以cosa=4/5,tana=-3/4,(sinπ/4=√2/2,cosπ/4=√2/2,tanπ/4=1)
sin(π/4-a)
=sinπ/4·cosa-cosπ/4·sina
=√2/2·4/5-√2/2·(-3/5)
=√2/10
同理,可算出cos(π/4+a)=(7√2)/10
tan(a-π/4)
=(tana-tanπ/4)/(1+tanatanπ/4)
=(-3/4-1)·(1+-3/4*1)
=-7/16
过程就是这样,不知道是否有算错的地方,你自己在检验一下
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