Given sinx= -1/8 and tanx<0. find sin2x

Answer 1

since sin<0 and tan<0, we are in QIV

if sinx = -1/8, then cosx = √63/8, so

sin2x = 2sinx*cosx = 2(-1/8)(√63/8) = -√63/32

makes sense, since if sinx is -1/8, x is close to 2pi, so 2x is close to 4pi, still in QIV.