Question #d4766

1 Answer
Apr 1, 2017

#sin (x/2) = - sqrt(9 + sqrt17)/(3sqrt2)#

Explanation:

#sin x = - 8/9#
#cos^2 x = 1 - sin^2 x = 1 - 64/81 = 17/81 #
#cos x = - sqrt17/9# (because x is in Quadrant 3)
Use trig identity:
#2sin^2 (x/2) = 1 - cos x = 1 + sqrt17/9 = (9 + sqrt17)/9#
#sin^2 (x/2) = (9 + sqrt17)/18#
#sin (x /2) = +- sqrt(9 + sqrt17)/(3sqrt2)#
Because x is in Quadrant 3, take the negative value.