how do you find the exact value of sin 3pi/8 using the half-angle formula

Question

 I really don't understand what to do.

Answer 1

Well 3pi/8  is  one half of   3pi/4   (aka  135 degrees)

 

The formula is   sin( 3pi/8)  = sin(  (3pi/4) /2) =  sqrt( ( 1- cos(3pi/4) )/2)  

  { the positive square root is taken because  3pi/8 is in the first quadrant.  }

 

  cos (3pi/4) =    - sqrt(2)/2     So

 

 sin( 3pi/8) =  sqrt(( 1 + sqrt(2)/2 ) /2)