已知 sina=1/3,sinb=1/2,(ab皆为锐角),则sin(a+b)=______

问题描述:

已知 sina=1/3,sinb=1/2,(ab皆为锐角),则sin(a+b)=______

sina=1/3,cosa=2√2/3
sinb=1/2 cosb=√3/2
sin(a+b)
=sinacosb+sinbcosa
=(1/3)*(√3/2)+(1/2)*(2√2/3)
=√3/6+2√2/6
=(√3+2√2)/6