Question

Question #42131

Answer 1

`sqrt(2 + sqrt3)/2`

Explanation:

Unit circle and property of complement arcs -->
`sin ((5pi)/12) = sin (-pi/12 + (6pi)/12) =`
`= sin (-pi/12 + pi/2) = cos (pi/12)`
Find `cos (pi/12)` by using trig identity:
`2cos^2 a = 1 + cos 2a`
In this case:
`2cos^2 (pi/12) = 1 + cos (pi/6) = 1 + sqrt3/2 = (2 + sqrt3)/2`
`cos^2 (pi/12) = (2 + sqrt3)/4`
`cos (pi/12) = +- sqrt(2 + sqrt3)/2`
Since `pi/12` is in Quadrant 1, take the positive value.
Finally,
`sin ((5pi)/12) = cos (pi/12) = sqrt(2 + sqrt3)/2`