已已知向量a=(sinπx/2,sinπ/3),向量b=(cosπx/2,cosπ/3),且向量a与向量b共线
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已已知向量a=(sinπx/2,sinπ/3),向量b=(cosπx/2,cosπ/3),且向量a与向量b共线
如果角0<A<B<π,且A+B+C=π,满足f(4A/π)=f(4B/π)=1/2 求sinB/sinC的值
如果角0<A<B<π,且A+B+C=π,满足f(4A/π)=f(4B/π)=1/2 求sinB/sinC的值
∵向量a∥向量b,∴sin(πx/2)cos(π/3)-sin(π/3)cos(πx/2)=0.
sin(πx/2-π/3)=0.
πx/2-π/3=0.
x=2/3.
令f(x)=sin(πx/2-π/3).
则 f(4A/π=f(4B/π)=1/2.
即,sin[(π/2)*4A/π-π/3]=sin[π/2*4B/π-π/3}=sin(π/6) ,[或=sin5π/6].
∴ 2A-π/3=π/6
∴2A=π/6+π/3.
=π/2.
∴Aπ/4.
∵题设0<A<B<π.
∴2B-π/3=π/5.
2B=5π/6+π/3.
=7π/6.
∴B=7π/12.
∵A+B+C=π.
C=π-A-B=π-π/4-7π/12.
∴C=π/6.
sinB/sinC=(sinπ/4)/(sinπ/6).
∴sinB/sinC=√2.
sin(πx/2-π/3)=0.
πx/2-π/3=0.
x=2/3.
令f(x)=sin(πx/2-π/3).
则 f(4A/π=f(4B/π)=1/2.
即,sin[(π/2)*4A/π-π/3]=sin[π/2*4B/π-π/3}=sin(π/6) ,[或=sin5π/6].
∴ 2A-π/3=π/6
∴2A=π/6+π/3.
=π/2.
∴Aπ/4.
∵题设0<A<B<π.
∴2B-π/3=π/5.
2B=5π/6+π/3.
=7π/6.
∴B=7π/12.
∵A+B+C=π.
C=π-A-B=π-π/4-7π/12.
∴C=π/6.
sinB/sinC=(sinπ/4)/(sinπ/6).
∴sinB/sinC=√2.
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