Posted by **Mandy** on Monday, May 3, 2010 at 2:07pm.

Please help me solve this problem. I have a test tomorrow and I do not understand at all.

Determine all solutions of the equations in radians.

Find cos x/2, given that cos x = 1/4 and x terminates in 0 < x < π/2.

- trig -
**Reiny**, Monday, May 3, 2010 at 3:52pm
let's use

cos 2A = 2cos^2 A - 1

or

cos x = 2cos^2(x/2) - 1

1/4 = 2cos^2(x/2) - 1

5/8 = cos^2(x/2)

cosx = √5/√8 or √10/4

- For Reiny -
**Mandy**, Monday, May 3, 2010 at 4:11pm
How did you get 5/8? Thanks for your help!

- trig -
**Reiny**, Monday, May 3, 2010 at 4:37pm
from

1/4 = 2cos^2(x/2) - 1

1/ 4 + 1 = 2cos^2(x/2)

5/4 = 2cos^2(x/2) , now divide by 2

5/8 = cos^2(x/2) , now take √

cos x/2 = √5/√8 , rationalizing

cos x/2 = (√5/√8)(√8/√8) = √40/8 = 2√10/8 = √10/4

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