Question 6

Question

Given 90< theta<180 and cos(theta)=-5/13, which is sin theta/2?

Answer 1

90< theta<180

45<theta/2<90

theta/2 is in 1st quadrant.

sin(theta/2) is positive.

sin(theta/2)=sqrt((1-costheta)/2)

                 =sqrt((1-(-5/13)/2)

                 =sqrt((1+(5/13)/2)

                 =sqrt((18/13)/2)

                 =sqrt(18/26)