Question

Question #00444

Answer 1

`sqrt(2 - sqrt3)/2`

Explanation:

`cos ((19pi)/12) = cos ((-5pi/12 + 2pi) = cos (5pi)/12 =`
`= cos (-pi/12 + pi/2) = sin (pi/12).`
Find `sin (pi/12)` by using the trig identity:
`2sin^2 (pi/12) = 1 - cos pi/6) = 1 - sqrt3/2 = (2 - sqrt3)/2`
`sin^2 (pi/12) = (2 - sqrt3)/4`
`sin (pi/12) = +- sqrt(2 - sqrt3)/2`
since `sin (pi/12)` is positive, therefor,
`cos ((19pi)/12) = sin (pi/12) = sqrt(2 - sqrt3)/2`