find tantheta2 if cos4041 and 90deg

find tan(theta/2) if cos=40/41 and -90deg<theta<0

Solution

tan(theta/2)=(1-cos theta)/sin theta

cos theta= 40/41

adjacent=40 and hypotenuse=41

opposite=sqrt(hypotenuse^2 - adjacent^2)= 9

sin theta=opposite/hypotenuse=-9/41

tan (theta/2)=(1-40/41)/(9/41)= -1/9