multiple Angle identities

Question

if s/2 is in the third quadrant and cos s = -8/17, what is cos s/2?

Answer 1

cos s/2 = ±√((1 + cos s) / 2))

cos s/2 = ±√((1 - 8/17) / 2))

cos s/2 = ±√((9/17) / 2))

cos s/2 = ±√(9/34)

cos s/2 = ±(3√34) / 34

 

Since s/2 is in QIII, the negative value is used.