已知sina=5/13,a∈（π/2,π）,则sin2a=?cos2a=?tan2a=?sina/2=、cosa/2=?tana/2=?

题目

已知sina=5/13,a∈（π/2,π）,则sin2a=?cos2a=?tan2a=?sina/2=、cosa/2=?tana/2=?

答案

sina=5/13,a∈（π/2,π）,cosa=-根号[1-(sina)^2]=-12/13,sin2a=2sina*cosa=-120/169,cos2a=1-2(sina)^2=119/169,tan2a=sin2a/cos2a=-120/119 a/2∈（π/4,π/2）sina/2=根号[(1-cosa)/2]=5带根号26/26 cosa/2=根号[(1+cosa)/2]=根号26/26,tana/2=5