Question 671744
If csc x = 5, 90 degrees < x < 180 degrees. 
a. sin (x/2) =? 
b. cos (x/2) =? 
c. tan (x/2) =?
find exact values 
**
sinx=1/cscx=1/5=opp side/hypotenuse
adj side=&#8730;(5^2-1^2)=&#8730;(25-1)=&#8730;24
cosx=-&#8730;24/5
tanx=opp side/adj side=-1/&#8730;24
you are working with a reference angle in quadrant II where sin is>0, cos<0, and tan<0
..
Identities: 
sin(x/2)=±&#8730;[(1-cosx)/2]
=&#8730;[(1+&#8730;24/5)/2]
=&#8730;[(5+&#8730;24)/5)/2]
sin(x/2)=&#8730;[(5+&#8730;24)/10]
..
cos (x/2) =±&#8730;[(1+cosx)/2]
=&#8730;[(1-&#8730;24/5)/2]
=&#8730;[(5-&#8730;24/5)/2]
=&#8730;[(5-&#8730;24)/10]
..
tan (x/2)=sinx/(1+cosx)
=[(1/5)/(1-&#8730;24/5)]
=1/(5-&#8730;24)