SOLUTION: If csc x = 5, 90 degrees < x < 180 degrees. a. sin (x/2) =? b. cos (x/2) =? c. tan (x/2) =? So far I have sin = 1/5, but I have no idea what to do after.

Question 671744: If csc x = 5, 90 degrees < x < 180 degrees.
a. sin (x/2) =?
b. cos (x/2) =?
c. tan (x/2) =?
So far I have sin = 1/5, but I have no idea what to do after.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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=√(5^2-1^2)=√(25-1)=√24
cosx=-√24/5
tanx=opp side/adj side=-1/√24
you are working with a reference angle in quadrant II where sin is>0, cos<0, and tan<0
..
Identities:
sin(x/2)=�√[(1-cosx)/2]
=√[(1+√24/5)/2]
=√[(5+√24)/5)/2]
sin(x/2)=√[(5+√24)/10]
..
cos (x/2) =�√[(1+cosx)/2]
=√[(1-√24/5)/2]
=√[(5-√24/5)/2]
=√[(5-√24)/10]
..
tan (x/2)=sinx/(1+cosx)
=[(1/5)/(1-√24/5)]
=1/(5-√24)
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