If sina=-5/8 with 270<a<360 determine sina/2

Question

the correct answer is: (1/4)(sqrt(8-sqrt(39))

I'm unsure how they got the eight and the 1/4

Answer 1

sinA= -5/8, A in quadrant IV sines negative, cosines positive

cosA = sqr(64-25)/8 = sqr39/8

general half angle formula for sin(A/2) = +/- sqr((1-cosA)/2) substitute (sqr39)/8 for cosA

sinA/2 = -sqr(1-cosA)/2) = sqr(1-sqr39/8)/2) =sqr(8-sqr39)/16)= (1/4)sqr(8-sqr39)