Given sin theta 13 pi Solution6 sin theta 13 Here theta is

Solution

6. sin theta =-1/3

Here theta is in third quadrant

opposite=1 and hypotenuse=3

Adjacent=sqrt(9-1)=sqrt8=2sqrt2

Cos theta=-2sqrt2/3

theta is in third quadrant. Therefore theta/2 is in second quadrant. And in second quadrant cos is negative

cos²theta/2= 1/2(1+cos theta)

                = 1/2(1-2sqrt2/3) =(3-2sqrt2)/6

cos theta/2= -sqrt(3-2sqrt2)/6