Find sin(u/2) if sin u = 0.231 and u is in Quadrant-II.

Question

if      and  is in Quadrant-II.

answer 4 decimal places.

Answer 1

Using the half angle identity

sin(u/2) = √((1-cos(u))/2) This will be positive since u/2 will be in QI if u is in QII.

sin(u) = .231/1 --> cos(u)= √(1-.231²) = 0.9730

sin(u/2) = √((1-0.9730)/2) = 0.0822

Answer 2

cosu = - √1 - 0.231² = - 0.97295375 becouse u in quadrant II.

sin(u/2) = √(1 - cosu)/2 = √(1 + 0.97295375)/2 = 0.7023