Use an appropriate compound angle formula to evaluate the following as an exact value.

Question

sin 11π/12

Answer 1

sin 11π / 12

sin (6π/12 + 5π/12)

sin (π/2 + 5π/12)

sin π/2 cos 5π/12 + cos π/2 sin 5π/12

cos 5π/12

cos (3π/12 + 2π/12)

cos (π/4 + π/6)

cos π/4 cos π/6 - sin π/4 sin π/6

Can you complete and answer?

Answer 2

sin ( (11/12) pi) =

sin [ (12/12)pi - (1/12) pi ] =

sin [ pi - (1/12) pi ] =

sin pi * cos (1/12) pi - cos pi * sin (1/12)pi =

0 * cos (1/12) pi - (-1) ( sin (1/12) pi) =

sin (1/12)pi =

sin ( 1/2 (pi/6)) =

sin ( T/2) where T = pi/6

= +or- sqrt( (1 - cos T)/2 )

= +or- sqrt( (1 - sqrt(3)/2) /2)

=

+or- sqrt( (2 - sqrt(3))/4 )

It will actually be negative there in quadrant 4