Question

How do you evaluate `cos((11pi) / 12)`?

Answer 1

`sqrt(2 + sqrt3)/2`

Explanation:

On the trig unit circle,
`cos((11pi)/12) = cos (pi/12`).
Evaluate `cos (pi/12)` bu applying the identity:
`cos 2a = 2cos^2 a - 1`
`cos (pi/6) = sqrt3/2 = 2cos^2 (pi/12) - 1`
`2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2`
`cos^2 (pi/12) = (2 + sqrt3)/4`
`cos (pi/12) = sqrt(2 + sqrt3)/2` (`cos (pi/12)` is positive)