Question

How do you use half angle formula to simplify `sin (3pi)/8`?

Answer 1

The Half Angle Formula for Sin
`sin(theta) = 2*sin(theta/2)*cos(theta/2)`

Note that `(3pi)/2`
(in standard position, with the base side along the positive x-axis)
has its terminal side along the negative y-axis
and
`sin((3pi)/2) = -1`

`cos((3pi)/2) = 0`

So
`sin(3pi) = (2*(-1)*(0))/8`

`= 0`