Question 864414
Use the given information to find each value 
cos t = 5/13 , 0 < t < pi/2 
cos 2t= 
sin 2t = 
cos t/2 = 
sin t/2 =
***
You are working with a (5-12-13) reference right triangle in quadrant I.
sin t =12/13
cos 2t=cos^2t-sin^2t=25/169-144/169=-119/169
sin 2t=2sin t*cos t=2*12/13*5/13=120/169
{{{cos(t/2)=sqrt((1+cos t)/2)=sqrt((1+(5/13)/2))=sqrt(((18/13)/2))=sqrt(18/26)=sqrt(9/13)=3/sqrt(13)}}}
{{{sin(t/2)=sqrt((1-cos t)/2)=sqrt((1-(5/13)/2))=sqrt(((8/13)/2))=sqrt(8/26)=sqrt(4/13)=2/sqrt(13)}}}