Question 546902
Use double-angle identities to find values of the sine and cosine functions for each angle measure. Find sin theta and cos theta given cos 2 theta = 5/13 and 0 < theta < pi/2 
cos theta:
sin theta:
..
use x in place of theta
Use half-angle formulas:
cos(2x)=5/13
cos(x)=cos(2x/2)=&#8730;[(1+cos(2x))/2]=&#8730;[(1+5/13)/2]=&#8730;[(18/13)/2]
=&#8730;[(18/26]=&#8730;(9/13)=3/&#8730;13
cos(x)=(3/&#8730;13)
..
sin(2x)=12/13 (by pythagorean theorem)
sin(x)=sin(2x/2)=&#8730;[(1-cos(2x))/2]=&#8730;[(1-5/13)/2]=&#8730;[(8/13)/2]
=&#8730;[(8/26]=&#8730;(8/26)=&#8730;(4/13)
sin(x)=&#8730;(4/13)