Find sin x/2 if cos x=-31/49 and x is between pi and 2pi?

1 Answer
Dec 7, 2017

#sin (x/2) = (2sqrt10)/7#

Explanation:

Use trig identity:
#2sin^2 (x/2) = 1 - cos x #
In this case:
#2sin^2 (x/2) = 1 + 31/49 = 80/49#
#sin^2 (x/2) = 40/49#
#sin (x/2) = +- (2sqrt10)/7#
Because x is in Quadrant 3, or Quadrant 4, #x/2# is in Q. 2 or Q. 1, so, #sin (x/2)# is positive.
#sin (x/2) = (2sqrt10)/7#