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

## Answer this Question

## Related Questions

- Precal - I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A...
- Trigonometry - I have some trigonometric equations to do, but I'm pretty lost, ...
- trig - I'm confused with this concept: Okay, so I have this problem: cos2x( 2 ...
- solving trig. equations - tan(3x) + 1 = sec(3x) Thanks, pretend 3x equals x so ...
- trig - I need to find all solutions of the given equations for the indicated ...
- trig - 2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3&#...
- trig equations - Find all solutions (if they exist)for the given equation on the...
- Physics (Calc Based) - I understand how to solve this problem ,however cannot ...
- math help, test tomorrow!!! - For 0 <or equal B <or equal 2 pi determine ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...