已知sina=5⼀13,π⼀2<a<π,求cosa,sin(a-π⼀3),sina⼀2的值,请写过城

2024-12-25 11:14:26
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回答1:

sina=5/13,π/2因为,sin²a+cos²a=1,且cosa<0
所以,cosa=-12/13

sin(a-π/3)
=(sina)(cosπ/3)-(cosa)(sinπ/3)
=(5/13)(1/2)-(-12/13)(√3/2)
=(5+12√3)/26

π/2sin(a/2)>0
又,cosa=1-2sin²(a/2)
sin²(a/2)=(1-cosa)/2=(1+12/13)/2=25/26
所以,sin(a/2)=(5√26)/26