sin u 513 pi2 u Find the exact values of sinu2 cosu2 and

sin u = 5/13 , pi/2 < u < Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas.

Solution

/2 < u <

/4 < u/2 < /2

sin u = 5/13

cos u =-[13²-5²] /13 =-12/13

sin(u/2)=[(1-cosu)/2]

sin(u/2)=[(1+(12/13))/2]

sin(u/2)=(25/26)

cos(u/2)=[(1+cosu)/2]

cos(u/2)=[(1-(12/13))/2]

cos(u/2)=(1/26)

tan(u/2)=sin(u/2)/cos(u/2)

tan(u/2)=(25/26)/(1/26)

tan(u/2)=(25)

tan(u/2)=5