Posted by john 2020 on Thursday, March 18, 2010 at 11:16pm.
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, Thursday, March 18, 2010 at 11:58pm
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, Friday, March 19, 2010 at 12:03am
can u simplify the answer any more?????

Correction  precal  Reiny, Friday, March 19, 2010 at 12:15am
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, Friday, March 19, 2010 at 12:17am
thank u
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