sin(a)=5/13.a+b=45度,求sin(b).

题目

sin(a)=5/13.a+b=45度,求sin(b).
如题.

答案

sin(a)=5/13→cos(a)=12/13
sin(a+b)=sin45°=√2/2
=sin(a)cos(b)+cos(a)sin(b)
=5/13·cos(b)+12/13·sin(b)
cos(a+b)=cos45°=√2/2
=cos(a)cos(b)-sin(a)sin(b)
=12/13·cos(b)-5/13·sin(b)
两式相等简化后为：
17sin(b)=7cos(b) ……①
另：sin(b)^2+cos(b)^2=1 ……②
联合①、②解出：
sin（b）=7/√338