Question

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

Answer 1

What is `(5pi)/12` half of?

It is half of its double: `2 xx (5pi)/12 = 2/1*(5pi)/12 =(5pi)/6`

`sin(1/2x) = +-sqrt((1-cosx)/2)`

We know that `(5pi)/12` is in quadrant I, so it has positive sine,

`sin((5pi)/12) = sin(1/2((5pi)/6)) = sqrt((1-cos((5pi)/6))/2)`

`= sqrt((1-sqrt3/2)/2) = sqrt((2-sqrt3)/4) = sqrt(2-sqrt3)/2`