Question 843989
if cos x = 1/9 and x is an obtuse angle, find sin 1/2 x
{{{sin(1/2)(x)=sin(x/2)=sqrt((1-cos(x))/2)=sqrt((1-(1/9))/2)
=sqrt((8/9)/2)=sqrt(4/9)=2/3}}}
sin(1/2)x=2/3 (in quadrant II where sin>0)
calculator check:
cos(x)=1/9 (in quadrant IV)
x=360-83.62≈276.38˚
x/2≈138.19˚
sin(x/2)=sin(138.19)≈0.6666..≈2/3