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August 21, 2014

August 21, 2014

Posted by **john 2020** on Thursday, March 18, 2010 at 11:16pm.

csc u=-6/5, tan u is greater than 0

Find cos u/2

- precal -
**Reiny**, Thursday, March 18, 2010 at 11:58pmcsc 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 12:03amcan u simplify the answer any more?????

- Correction - precal -
**Reiny**, Friday, March 19, 2010 at 12:15amI 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 12:17amthank u

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