Question

sendo sen x = 1/3 e pi/2 < x > pi, calcular sen 2x

Answer 1

$senx=\frac{1}{3}\\senx^2+cosx^2=1\\\frac{1}{9}+cosx^2=1\\cosx^2=\frac{9}{9}\frac{-1}{9}\\cosx=\frac{ \sqrt{8} }{ \sqrt{9} }\\cosx=\frac{ \sqrt{8} }{3}\\sen(ab+b)=sena.cosb+senb.cosa\\sen(x+x)=senx,cosx+senx.cosx\\sen2x=2senxcosx\\sen2x=2.\frac{1}{3}.\frac{ \sqrt{8} }{3}\\sen2x=\frac{2 \sqrt{8} }{9}$