Question

How do you find the value of `sin ((11pi)/12)`?

Answer 1

`sqrt3/2`

Explanation:

Trig table and unit circle -->
`sin ((11pi)/12) = sin (-pi/12 + (12pi)/12 = sin (-pi/12 + pi) =`
`= sin (pi/12)`.
Use trig identity;
`2sin^2 = 1 + cos pi/6 = 1 + 1/2 = 3/2`
`sin^2 (pi/12) = 3/4`
`sin (pi/12) = sqrt3/2` (because sin (pi/12) is positive)
Finally, `sin ((11pi)/12) = sin (p/12) = sqrt3/2`