Question

若tan(2pai-a)=根号5/2,且a属于(-pai/2,0),sin(pai+a)=?坐等

Answer 1

∵a属于(-π/2,0)

∴sina-tana=√5/2

==>tana=-√5/2

==>sina/cosa=-√5/2

==>sina=-(√5/2)cosa

==>(-(√5/2)cosa)²+cos²a=1 (∵sin²a+cos²a=1)

==>(9/4)cos²a=1

==>cos²a=4/9

∴sina=-√(1-cos²a)=-√(1-(4/9)²)=-√5/3

故sin(π+a)=-sina=-(-√5/3)=√5/3.