1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值
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![1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值](/uploads/image/z/1170032-32-2.jpg?t=1%2C%E5%B7%B2%E7%9F%A5sin%28a-b%29cosa-cos%28b-a%29sina%3D3%2F5%2Cb%E6%98%AF%E7%AC%AC%E4%B8%89%E8%B1%A1%E9%99%90%E8%A7%92%2C%E6%B1%82sin%28b%2B5pi%2F4%29%E7%9A%84%E5%80%BC)
1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值
1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值
1,已知sin(a-b)cosa-cos(b-a)sina=3/5,b是第三象限角,求sin(b+5pi/4)的值
sin(a-b)cosa-cos(b-a)sina=sin(a-b-a)=sin(-b)=-sin(b)=3/5;
sin(b)=-3/5;b是第三象限角,cos(b)=-4/5;
sin(b+5pi/4)=-sin(b+pi/4)=-sqrt(2)/2*(sin(b)+cos(b))=7*sqrt(2)/10
sqrt表示根号
因为cos(b-a)=cos(a-b)
所以
sin(a-b)cosa-cos(b-a)sina
=sin(a-b)cosa-cos(a-b)sina
=sin(a-b-a)
=sin(-b)
sinb
=-3/5
因为b是第三象限角,所以cosb=-4/5
sin(b+5pi/4)
=sin(b+pi/4+pi)
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因为cos(b-a)=cos(a-b)
所以
sin(a-b)cosa-cos(b-a)sina
=sin(a-b)cosa-cos(a-b)sina
=sin(a-b-a)
=sin(-b)
sinb
=-3/5
因为b是第三象限角,所以cosb=-4/5
sin(b+5pi/4)
=sin(b+pi/4+pi)
=-sin(pi/4+b)
=-(sin pi/4 * cosb+ cos pi/4 * sinb)
=(√2)/2 * 7/5
=10 分之 7*√2
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