Find the exact value of sin 11?/12.

Question

I'm stuck on this problem.

Answer 1

Should this be sin(11 pi/12)?

 

11 pi/12 is in 4th quadrant where sine is negative.

 

sin(11 pi/6/2) = –√(( 1-cos(11 pi/6) )/2)

 

cos(11 pi/6) = cos(12 pi/6 - pi/6)

 

= cos(- pi/6) = cos(pi/6) = √(3)/2

 

sin(11 pi/6/2) = –√(( 1-√(3)/2 )/2)

 

= –√( ( 2-√(3) )/4)

 

= –(1/2)√( 2-√(3) )