Use half-angle formulas to find an exact value for the following. sin 22.5°

Answer 1

sin(α/2​)=±√[(1−cosα)/2​]

Let α=45

sin(45/2​)=±√[(1−√2/2)/2​]

sin 22.5 = ±√[(2/2−√2/2)/2​]

sin 22.5 =±√[(2−√2)/2)/2​]

sin 22.5 =±√[(2−√2)/4)​]

Answer 2

sin(x/2)= sqr (1-cosx)/2

sin(22.5) = sqr(1-cos45)/2

=sqr(1-1/sqr2)/2

=(1/2)sqr(2-sqr2)

You can ignore the negative square roots, as 22.5 is half of 45 degrees which has positive sines & cosines