# precal

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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 -

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 -

can u simplify the answer any more?????

• Correction - precal -

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 -

thank u

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