已知向量a=(cos(3/2)x,sin(3/2)x),向量b=(-sin(x/2),-cos(x/2)),x属于90度
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已知向量a=(cos(3/2)x,sin(3/2)x),向量b=(-sin(x/2),-cos(x/2)),x属于90度到180度
1
a+b=(cos(3x/2)-sin(x/2),sin(3x/2)-cos(x/2))
所以:|a+b|^2=(cos(3x/2)-sin(x/2))^2+(sin(3x/2)-cos(x/2))^2
=2-2(cos(3x/2)*sin(x/2)+sin(3x/2)*cos(x/2))=2-2sin(2x)=3
即:sin(2x)=-1/2,因:x∈[π/2,π],所以:2x∈[π,2π]
故:2x=7π/6或2x=11π/6,即:x=7π/12或x=11π/12
2
a dot b=-cos(3x/2)*sin(x/2)-sin(3x/2)*cos(x/2)=-sinx(2x)
所以:f(x)=-sinx(2x)+2-2sin(2x)=2-3sin(2x)
在x∈[π/2,π],即:2x∈[π,2π]时,sin(2x)∈[-1,0]
所以:2-3sin(2x)∈[2,5],因:c>f(x),所以c>5
a+b=(cos(3x/2)-sin(x/2),sin(3x/2)-cos(x/2))
所以:|a+b|^2=(cos(3x/2)-sin(x/2))^2+(sin(3x/2)-cos(x/2))^2
=2-2(cos(3x/2)*sin(x/2)+sin(3x/2)*cos(x/2))=2-2sin(2x)=3
即:sin(2x)=-1/2,因:x∈[π/2,π],所以:2x∈[π,2π]
故:2x=7π/6或2x=11π/6,即:x=7π/12或x=11π/12
2
a dot b=-cos(3x/2)*sin(x/2)-sin(3x/2)*cos(x/2)=-sinx(2x)
所以:f(x)=-sinx(2x)+2-2sin(2x)=2-3sin(2x)
在x∈[π/2,π],即:2x∈[π,2π]时,sin(2x)∈[-1,0]
所以:2-3sin(2x)∈[2,5],因:c>f(x),所以c>5
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