SOLUTION: If sin x = {{{12/13}}} where {{{pi/2 <= x <= pi}}}, determine: a) {{{sin (x/2)}}} b) {{{sec (x/2)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: If sin x = {{{12/13}}} where {{{pi/2 <= x <= pi}}}, determine: a) {{{sin (x/2)}}} b) {{{sec (x/2)}}}      Log On


   

Question 549871: If sin x = 12%2F13 where pi%2F2+%3C=+x+%3C=+pi, determine:
a) sin+%28x%2F2%29
b) sec+%28x%2F2%29
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If sin x =12/13, where pi/2 <= x <= pi, determine:
a) sin (x/2)
b) sec (x/2)
..
You are working with a reference angle in quadrant II where sin>0 and cos<0
sin x=12/13 (given)
cosx=-5/13
..
a) Using half-angle formula for sin
sin x/2=√[(1-cosx)/2]=√[(1+5/13)/2]=√[(18/13)/2]=√[(18/26]
..
b) Using half-angle formula for cos then taking the reciprocal
cos x/2=-√[(1-cosx)/2]=-√[(1-5/13)/2]=-√[(8/13)/2]=-√[(8/26]
sec x/2=1/(cos x/2)=-√(26/8)