Posted by john 2020 on .
use the given info. to find the exact value of the trig function.
csc u=6/5, tan u is greater than 0
Find cos u/2

precal 
Reiny,
csc u = 6/5
sinu = 5/6
by Pythagoras, and knowing sin u is negative and tan u is positive
cosu = √11/6
we know cosA = 1  2cos^2(A/2)
or
cosu = 1  2cos^2(u/2)
√11/6 = 1  2cos^2(u/2)
2cos^2(u/2) = 1 + √11/6)
cos u/2 = √[(1 + √11/6)/2]
check my arithmetic, 
precal 
john 2020,
can u simplify the answer any more?????

Correction  precal 
Reiny,
I had the formula backwards, ...
Should have been
cos A = 2cos^2(A/2)  1
or
cos u = 2cos^2 (u/2)  1
√11/6 + 1 = 2cos^2 (u/2)
√[1  √11/6)/2] = cos (u/2)
I picked the negative value, since we knew u was in III, so u/2 was in II, and in II the cosine is negative.
Since you wanted the "exact" value, there is no point simplifying the above answer. 
precal 
john 2020,
thank u