Need help with a double angle question

If cos2x=12/13 and 2x is in the first quadrant, evaluate the six trigonometric functions for x, without your calculator. The answer is:

cos x= 5/√26; sec x=√26/5

sinx=1/√26; csc x=√26

tanx=1/5; cot x=5

How do I get these answers? Any help would be greatly appreciated.

Re: Need help with a double angle question

Do you know either the "double angle formulas" or the "half angle formulas"?

Re: Need help with a double angle question

since $\displaystyle 0 < 2x < \frac{\pi}{2}$ , then $\displaystyle 0 < x < \frac{\pi}{4}$

$\displaystyle \cos{x} = \sqrt{\frac{1 + \cos(2x)}{2}}$

$\displaystyle \sin{x} = \sqrt{\frac{1 - \cos(2x)}{2}}$

sub in the value given for $\displaystyle \cos(2x)$ ...

Re: Need help with a double angle question

Thanks guys, I got it now.