find the exact value of sin(-5π/12)

Answer 1

Half Angle Formula:

sin (½ x) = ±((1 - cos x)/2)^1/2

-5π/12= (½)(-5π/6)

The value is negative because it's located in the fourth quadrant:

sin (-5π/12) =sin (½ (-5π/6)) = -((1 - cos (-5π/6))/2)^1/2

= -((1 - (-√3 /2))/2)^1/2

= -(1 + √3 /2)/2)^1/2

=(-(2 + √3)/2)^1/2 /2

= -(1/4)(2^1/2 + 6^1/2)