Given sinalpha 78 and alpha is in quadrant IV find the exact

Given sin(alpha)= -7/8 and alpha is in quadrant IV, find the exact value of sin(alpha/2)

Note: you are not allowed to use decimals in your answer.

sin(alpha/2)=

Solution

cos(alpha) = 1 - sin^2(alpha) = 15/8

sin(alpha/2) = {1-cos(alpha)}/2 = [{8-15}/16]