Use the given information about theta to find the exact valu

Use the given information about theta to find the exact values of the following. Tan (theta)=12/5 where pi

Given , tanteta=12/5

Teta is in 3 quadrant both x and y are -ve

x=-12,y=-5

Sin(2teta)=2 costeta sinteta=2×12/13 ×5/13=120/169

Cos(2teta)=cos^2 teta-sin^2 teta=(5/13)^2-(12/13)^2=-119/16

,tan(2teta)=sin2teta/cos2teta=-120/119

sin(teta/2)=squareroot 1-cos(teta)/2=squareroot 1-(-5/13)/2=3/squareroot 13

Cos(teta/2)=square root (1+cos(teta))/2=squareroot 1+(-5/13)/2=2/squareroot13

Tan(teta/2)=squareroot 1 - costeta /squareroot 1+costeta=3/2