Question

How do you use the half angle formula for sin (5π/12)?

Answer 1

The half angle formula is:
sin x/2 = +/- √ (( 1-cos x ) / 2 )
5π/12 = 5π/6 : 2
sin 5π/12 = +/- √(( 1 - cos ( 5π/6)) / 2 ) 
cos 5π/6 = cos 150° = -√3/2
$sin (5 \pi /12) = \sqrt{ \frac{1+ \sqrt{3}/2 }{2} } = \\ =\sqrt{ \frac{2+ \sqrt{3} }{4} } = \\ = \frac{ \sqrt{2+ \sqrt{3} } }{2} =$
≈ 0.966 ( this is sin 5π/12 )